From d793a6f8d6507b16dd9fe03714ed66143d25d960 Mon Sep 17 00:00:00 2001 From: Humphrey Yang Date: Tue, 31 Jan 2023 01:19:56 +1100 Subject: [PATCH 01/12] update lln_clt TODO --- in-work/lln_clt.ipynb | 864 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 864 insertions(+) create mode 100644 in-work/lln_clt.ipynb diff --git a/in-work/lln_clt.ipynb b/in-work/lln_clt.ipynb new file mode 100644 index 000000000..566c8435c --- /dev/null +++ b/in-work/lln_clt.ipynb @@ -0,0 +1,864 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "abbf8725", + "metadata": {}, + "source": [ + "## LLN and CLT\n", + "\n", + "## Overview\n", + "\n", + "This lecture illustrates two of the most important theorems of probability and statistics: The\n", + "law of large numbers (LLN) and the central limit theorem (CLT).\n", + "\n", + "These beautiful theorems lie behind many of the most fundamental results in econometrics and quantitative economic modeling.\n", + "\n", + "The lecture is based around simulations that show the LLN and CLT in action.\n", + "\n", + "We also demonstrate how the LLN and CLT break down when the assumptions they are based on do not hold.\n", + "\n", + "In addition, we examine several useful extensions of the classical theorems, such as\n", + "\n", + "* The delta method, for smooth functions of random variables, and\n", + "* the multivariate case.\n", + "\n", + "Some of these extensions are presented as exercises.\n", + "\n", + "We'll need the following imports:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "85a6731b", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import random\n", + "import numpy as np\n", + "import scipy.stats as st" + ] + }, + { + "cell_type": "markdown", + "id": "406e1374", + "metadata": {}, + "source": [ + "## Relationships\n", + "\n", + "\n", + "The LLN gives conditions under which sample moments converge to population moments as sample size increases.\n", + "\n", + "The CLT provides information about the rate at which sample moments converge to population moments as sample size increases.\n", + "\n", + "(lln_mr)=\n", + "## LLN\n", + "\n", + "```{index} single: Law of Large Numbers\n", + "```\n", + "\n", + "We begin with the law of large numbers, which tells us when sample averages\n", + "will converge to their population means.\n", + "\n", + "### The LLN in Action\n", + "\n", + "Let's see an example of the LLN in action before we go further.\n", + "\n", + "Consider a [Bernoulli random variable](https://en.wikipedia.org/wiki/Bernoulli_distribution) $X$ with parameter $p$.\n", + "\n", + "This means that $X$ takes values in $\\{0,1\\}$ and $\\mathbb P\\{X=1\\} = p$.\n", + "\n", + "We can think of drawing $X$ as tossing a biased coin where\n", + "\n", + "* the coin falls on \"heads\" with probability $p$ and\n", + "* we set $X=1$ if the coin is \"heads\" and zero otherwise.\n", + "\n", + "The mean of $X$ is \n", + "\n", + "$$\n", + "\\mathbb E X = 0 \\cdot \\mathbb P\\{X=0\\} + 1 \\cdot \\mathbb P\\{X=1\\} = \\mathbb P\\{X=1\\} = p\n", + "$$\n", + "\n", + "We can generate a draw of $X$ with `scipy.stats` (imported as `st`) as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "821a73c3", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1\n" + ] + } + ], + "source": [ + "p = 0.8\n", + "X = st.bernoulli.rvs(p)\n", + "print(X)" + ] + }, + { + "cell_type": "markdown", + "id": "c3146d09", + "metadata": {}, + "source": [ + "In this setting, the LLN tells us if we flip the coin many times, the fraction of heads that we see will be close to $p$.\n", + "\n", + "Let's check this:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "d95827fd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.79964\n" + ] + } + ], + "source": [ + "n = 1_000_000\n", + "X_draws = st.bernoulli.rvs(p, size=n)\n", + "print(X_draws.mean()) # count the number of 1's and divide by n" + ] + }, + { + "cell_type": "markdown", + "id": "e95b76a1", + "metadata": {}, + "source": [ + "If we change $p$ the claim still holds:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "404dbe87", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.300404\n" + ] + } + ], + "source": [ + "p = 0.3\n", + "X_draws = st.bernoulli.rvs(p, size=n)\n", + "print(X_draws.mean())" + ] + }, + { + "cell_type": "markdown", + "id": "78db68f3", + "metadata": {}, + "source": [ + "Let's connect this to the discussion above, where we said the sample average converges to the \"population mean\".\n", + "\n", + "The population mean is the mean in an infinite sample, which equals the true mean, or $\\mathbb E X$.\n", + "\n", + "The sample mean of the draws $X_1, \\ldots, X_n$ is\n", + "\n", + "$$\n", + "\\bar X_n := \\frac{1}{n} \\sum_{i=1}^n X_i\n", + "$$\n", + "\n", + "which, in this case, is the fraction of draws that equal one (the number of heads divided by $n$).\n", + "\n", + "Thus, the LLN tells us that\n", + "\n", + "```{math}\n", + ":label: exp\n", + "\n", + "\\bar X_n \\to \\mathbb E X = p\n", + "\\qquad (n \\to \\infty)\n", + "```\n", + "\n", + "This is exactly what we illustrated in the code above." + ] + }, + { + "cell_type": "markdown", + "id": "3faf5ee2", + "metadata": { + "jp-MarkdownHeadingCollapsed": true, + "tags": [] + }, + "source": [ + "(lln_ksl)=\n", + "### Statement of the LLN\n", + "\n", + "Let's state the LLN more carefully.\n", + "\n", + "The traditional version of the law of large numbers concerns independent and identically distributed (IID) random variables.\n", + "\n", + "Let $X_1, \\ldots, X_n$ be independent and identically distributed random variables.\n", + "\n", + "This random variables can be continuous or discrete.\n", + "\n", + "For simplicity we will assume they are continuous and we let $f$ denote their density function, so that, for any $i$ in $\\{1, \\ldots, n\\}$\n", + "\n", + "\n", + "$$ \n", + " \\mathbb P\\{a \\leq X_i \\leq b\\} = \\int_a^b f(x) dx\n", + "$$\n", + "\n", + "(For the discrete case, we need to replace densities with probability mass functions and integrals with sums.)\n", + "\n", + "Let $\\mu$ denote the common mean of this sample:\n", + "\n", + "$$\n", + " \\mu := \\mathbb E X = \\int_{-\\infty}^{\\infty} x f(dx)\n", + "$$\n", + "\n", + "In addition, let\n", + "\n", + "$$\n", + "\\bar X_n := \\frac{1}{n} \\sum_{i=1}^n X_i\n", + "$$\n", + "\n", + "TODO -- use a theorem environment (```{prf:theorem}...```)\n", + "\n", + "The law of large numbers (specifically, Kolmogorov's strong law) states that, if $\\mathbb E |X|$ is finite, then\n", + "\n", + "```{math}\n", + ":label: lln_as\n", + "\n", + "\\mathbb P \\left\\{ \\bar X_n \\to \\mu \\text{ as } n \\to \\infty \\right\\} = 1\n", + "```\n", + "\n", + "### Comments on the Theorem\n", + "\n", + "What does this last expression mean?\n", + "\n", + "Let's think about it from a simulation perspective, imagining for a moment that\n", + "our computer can generate perfect random samples (which of course [it can't](https://en.wikipedia.org/wiki/Pseudorandom_number_generator)).\n", + "\n", + "Let's also imagine that we can generate infinite sequences so that the statement $\\bar X_n \\to \\mu$ can be evaluated.\n", + "\n", + "In this setting, {eq}`lln_as` should be interpreted as meaning that the probability of the computer producing a sequence where $\\bar X_n \\to \\mu$ fails to occur\n", + "is zero." + ] + }, + { + "cell_type": "markdown", + "id": "72ef82c2", + "metadata": { + "tags": [] + }, + "source": [ + "### Illustration\n", + "\n", + "```{index} single: Law of Large Numbers; Illustration\n", + "```\n", + "\n", + "Let's now illustrate the LLN using simulation.\n", + "\n", + "When we illustrate it, we will use a key idea: the sample mean $\\bar X$ is itself a random variable.\n", + "\n", + "In a sense this is obvious but it can be easy to forget.\n", + "\n", + "The reason $\\bar X_n$ is a random variable is that it's a function of the random variables $X_1, \\ldots, X_n$.\n", + "\n", + "What we are going to do now is \n", + "\n", + "1. Pick some distribution to draw each $X_i$ from \n", + "1. Set $n$ to some large number\n", + "1. Generate the draws $X_1, \\ldots, X_n$\n", + "1. Calculate the sample mean $\\bar X_n$ and record its value in an array `sample_means`\n", + "1. Go to step 3\n", + "\n", + "We will continue the loop over steps 3-4 a total of $m$ times, where $m$ is some large integer.\n", + "\n", + "The array `sample_means` will now contain $m$ draws of the random variable $\\bar X_n$.\n", + "\n", + "If we histogram these observations of $\\bar X_n$, we should see that they are clustered around the population mean $\\mathbb E X$.\n", + "\n", + "Moreover, if we repeat the exercise with a larger value of $n$, we should see that the observations are even more tightly clustered around the population mean.\n", + "\n", + "This is, in essence, what the LLN is telling us." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "9299240a", + "metadata": {}, + "outputs": [], + "source": [ + "def generate_histogram(X_distribution, n, m):\n", + " fig, ax = plt.subplots(figsize=(10, 6))\n", + "\n", + " def draw_means(X_distribution, n):\n", + "\n", + " # Step 3: Generate n draws: X_1, ..., X_n\n", + " X_samples = distribution.rvs(size=n)\n", + "\n", + " # Step 4: Calculate sample mean\n", + " return np.mean(X_samples)\n", + " \n", + " # Step 5: Loop m times\n", + " sample_means = np.array([draw_means(distribution, n) for i in range(m)])\n", + " print(f'The mean of sample mean is {round(np.mean(sample_means),2)}')\n", + " \n", + " # Generate a histogram\n", + " ax.hist(sample_means, bins=30, alpha=0.5, density=True)\n", + " mu = X_distribution.mean()\n", + " if not np.isnan(mu):\n", + " ax.axvline(x=5, ls=\"--\", lw=3, label=fr\"$\\mu = {mu}$\")\n", + " \n", + " ax.set_xlim(min(sample_means), max(sample_means))\n", + " ax.set_xlabel(r'$\\bar x$')\n", + " ax.set_ylabel('Density')\n", + " ax.set(title=fr'$n = {n}, m = {m}$')\n", + " ax.legend()\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "c3056496-bc32-45ca-b733-53a1a990692a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The mean of sample mean is 5.0\n" + ] + }, + { + "data": { + 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Step 1: Draw from a normal distribution\n", + "distribution = st.norm(loc=5, scale=2)\n", + "\n", + "# Step 2: Set n to some large number and generate samples and set m to a large number for iterations\n", + "generate_histogram(distribution, n=1000, m=1000)" + ] + }, + { + "cell_type": "markdown", + "id": "baedeccf-e5d5-432c-8bd6-5e02684c956a", + "metadata": {}, + "source": [ + "We can see that the distribution of $\\bar X$ is clustered around $\\mathbb E X$ as expected.\n", + "\n", + "We can increase values for `n` and `m` to see how the distribution changes" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "0b0da74f-1f3d-4b75-bb4a-86c85c4539bb", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The mean of sample mean is 5.0\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "generate_histogram(distribution, n=50_000, m=1000)" + ] + }, + { + "cell_type": "markdown", + "id": "e497302a-21fd-4220-ab7f-2fdd44b7941e", + "metadata": {}, + "source": [ + "Let's see the result of a large number of $n$s to see the changes with an increasing $n$.\n", + "\n", + "You can imagine the result when extrapolating this trend for $(n \\to \\infty)$." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "597a28c8-046e-44d4-b4ce-4bf1d580601c", + "metadata": {}, + "outputs": [], + "source": [ + "def generate_multiple_hist(X_distribution, ns, m, log_scale=False):\n", + " _, ax = plt.subplots(figsize=(10, 6))\n", + "\n", + " def draw_means(X_distribution, n):\n", + " X_samples = X_distribution.rvs(size=n)\n", + " return np.mean(X_samples)\n", + " \n", + " for n in ns:\n", + " sample_means = [draw_means(X_distribution, n) for i in range(m)]\n", + " if log_scale:\n", + " plt.xscale('symlog')\n", + " ax.hist(sample_means, bins=60, alpha=0.4, density=True, label=fr'$n = {n}, m = {m}$')\n", + " \n", + " mu = X_distribution.mean()\n", + " if not np.isnan(mu):\n", + " ax.axvline(x=5, ls=\"--\", lw=3, label=fr\"$\\mu = {mu}$\")\n", + " \n", + " ax.set_xlim(min(sample_means), max(sample_means)) \n", + " ax.set_xlabel(r'$\\bar x$')\n", + " ax.set_ylabel('Density')\n", + " ax.set(title=fr'$n = {n}, m = {m}$')\n", + " ax.legend()\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "7dbed08d-3560-4f6d-8bb9-7c3ee75bab43", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "generate_multiple_hist(st.norm(loc=5, scale=2), ns=[20_000, 50_000, 100_000], m=10_000)" + ] + }, + { + "cell_type": "markdown", + "id": "22987bd7", + "metadata": {}, + "source": [ + "## Breaking the LLN\n", + "\n", + "We have to pay attention to the assumptions in the statement of the LLN when we apply it.\n", + "\n", + "As indicated by {eq}`lln_as`, LLN can break when $\\mathbb E |X|$ is not finite or is not well defined.\n", + "\n", + "We can demonstrate this using a simple simulation using a [Cauchy distribution](https://en.wikipedia.org/wiki/Cauchy_distribution) for which it does not have a well-defined $\\mu$.\n", + "\n", + "TODO\n", + "\n", + "* Illustrate by simulation that the LLN can fail when the population mean is not finite\n", + "* Illustrate by simulation that the IID assumption is important" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "838fbcc4-691c-45ed-bd20-a853f1953c7e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "generate_multiple_hist(st.cauchy(), ns=[20_000, 50_000, 100_000], m=10_000, log_scale=True)" + ] + }, + { + "cell_type": "markdown", + "id": "dddea715-be50-4d63-82e7-b51115b2c9cf", + "metadata": {}, + "source": [ + "We lost the convergence we have before for normal distribution\n", + "\n", + "A scattered plot can better show us why this is the case" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "dda56a48-d06c-4ed4-9c7e-180d843d1d63", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=(15, 6))\n", + "\n", + "def scattered_mean(distribution, burn_in, n, jump, ax, title, ylog=False):\n", + " \n", + " #Set a jump to reduce simulation complexity\n", + " sample_means = [np.mean(distribution.rvs(size=i)) \n", + " for i in range(burn_in, n+1, jump)]\n", + " \n", + " ax.scatter(range(burn_in, n+1, jump), sample_means, s=10)\n", + " if ylog:\n", + " ax.set_yscale(\"symlog\")\n", + " ax.set_title(title)\n", + " ax.set_xlabel(\"Sample Size\")\n", + " ax.set_ylabel(\"Sample Mean\")\n", + " return ax\n", + "\n", + "scattered_mean(distribution=st.cauchy(), \n", + " burn_in=10_000, \n", + " n=1_000_000, \n", + " ax=axes[0],\n", + " jump=1000,\n", + " title=\"Cauchy Distribution\",\n", + " ylog=True)\n", + "\n", + "scattered_mean(distribution=st.norm(), \n", + " burn_in=10_000, \n", + " n=1_000_000,\n", + " ax=axes[1],\n", + " jump=1000,\n", + " title=\"Normal Distribution\")\n", + "\n", + "fig.suptitle('Sample Mean with Different Sample Size')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "4e126f26-eb95-4c3c-b579-00edb27c826a", + "metadata": {}, + "source": [ + "We can see that unlike normal distribution, Cauchy distribution does not have a convergence that LLN implies.\n", + "\n", + "It is also not hard to conjecture that LLN can be broken when the IID assumption is violated.\n", + "\n", + "We can go through an example that involves" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "5a0232ff-da52-4374-8506-609593db6bd7", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "n = 1_000_000\n", + "\n", + "def iid_comparison(n, p):\n", + " samples = np.zeros(n+1)\n", + " X_draws = st.bernoulli.rvs(p, size=n)\n", + " _, ax = plt.subplots(figsize=(10, 6))\n", + "\n", + " for i in range(n):\n", + " if samples[i] > 5:\n", + " samples[i+1] = st.norm.rvs(loc=5, scale=2, size=1)\n", + " else:\n", + " samples[i+1] = st.norm.rvs(loc=10, scale=2, size=1)\n", + "\n", + " # Plot the stock prices without iid assumption\n", + " ax.hist(samples, label=\"non-iid\", bins=60, alpha=0.5, density=True)\n", + " distribution = st.norm\n", + " ax.hist(distribution.rvs(loc=5, scale=2, size=n), bins=60, label=\"iid\", alpha=0.5, density=True)\n", + "\n", + " # Add labels and legend\n", + " ax.set_xlabel(r'$\\bar x$')\n", + " ax.set_ylabel('Density')\n", + " ax.axvline(x=5, ls=\"--\", lw=3, label=fr\"$\\mu = {distribution.mean()}$\")\n", + " ax.legend()\n", + "\n", + " # Show the plot\n", + " plt.show()\n", + " \n", + "iid_comparison(n, 0.9)" + ] + }, + { + "cell_type": "markdown", + "id": "59934170", + "metadata": {}, + "source": [ + "## CLT\n", + "\n", + "```{index} single: Central Limit Theorem\n", + "```\n", + "\n", + "Next, we turn to the central limit theorem, which tells us about the distribution of the deviation between sample averages and population means.\n", + "\n", + "### Statement of the Theorem\n", + "\n", + "The central limit theorem is one of the most remarkable results in all of mathematics.\n", + "\n", + "In the IID setting, it tells us the following:\n", + "\n", + "TODO use a theorem environment (```{prf:theorem...```)\n", + "\n", + "(statement_clt)=\n", + "If the sequence $X_1, \\ldots, X_n$ is IID, with common mean\n", + "$\\mu$ and common variance $\\sigma^2 \\in (0, \\infty)$, then\n", + "\n", + "```{math}\n", + ":label: lln_clt\n", + "\n", + "\\sqrt{n} ( \\bar X_n - \\mu ) \\stackrel { d } {\\to} N(0, \\sigma^2)\n", + "\\quad \\text{as} \\quad\n", + "n \\to \\infty\n", + "```\n", + "\n", + "Here $\\stackrel { d } {\\to} N(0, \\sigma^2)$ indicates [convergence in distribution](https://en.wikipedia.org/wiki/Convergence_of_random_variables#Convergence_in_distribution) to a centered (i.e, zero mean) normal with standard deviation $\\sigma$.\n", + "\n", + "### Intuition\n", + "\n", + "```{index} single: Central Limit Theorem; Intuition\n", + "```\n", + "\n", + "The striking implication of the CLT is that for **any** distribution with\n", + "finite second moment, the simple operation of adding independent\n", + "copies **always** leads to a Gaussian curve." + ] + }, + { + "cell_type": "markdown", + "id": "928cdff7", + "metadata": {}, + "source": [ + "### Simulation 1\n", + "\n", + "Since the CLT seems almost magical, running simulations that verify its implications is one good way to build intuition.\n", + "\n", + "To this end, we now perform the following simulation\n", + "\n", + "1. Choose an arbitrary distribution $F$ for the underlying observations $X_i$.\n", + "1. Generate independent draws of $Y_n := \\sqrt{n} ( \\bar X_n - \\mu )$.\n", + "1. Use these draws to compute some measure of their distribution --- such as a histogram.\n", + "1. Compare the latter to $N(0, \\sigma^2)$.\n", + "\n", + "Here's some code that does exactly this for the exponential distribution\n", + "$F(x) = 1 - e^{- \\lambda x}$.\n", + "\n", + "(Please experiment with other choices of $F$, but remember that, to conform with the conditions of the CLT, the distribution must have a finite second moment.)\n", + "\n", + "(sim_one)=" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "c6444237", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Set parameters\n", + "n = 250 # Choice of n\n", + "k = 1_000_000 # Number of draws of Y_n\n", + "distribution = st.expon(2) # Exponential distribution, λ = 1/2\n", + "μ, s = distribution.mean(), distribution.std()\n", + "\n", + "# Draw underlying RVs. Each row contains a draw of X_1,..,X_n\n", + "data = distribution.rvs((k, n))\n", + "# Compute mean of each row, producing k draws of \\bar X_n\n", + "sample_means = data.mean(axis=1)\n", + "# Generate observations of Y_n\n", + "Y = np.sqrt(n) * (sample_means - μ)\n", + "\n", + "# Plot\n", + "fig, ax = plt.subplots(figsize=(10, 6))\n", + "xmin, xmax = -3 * s, 3 * s\n", + "ax.set_xlim(xmin, xmax)\n", + "ax.hist(Y, bins=60, alpha=0.4, density=True)\n", + "xgrid = np.linspace(xmin, xmax, 200)\n", + "ax.plot(xgrid, st.norm.pdf(xgrid, scale=s), 'k-', lw=2, label='$N(0, \\sigma^2)$')\n", + "ax.legend()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "48f02fa4", + "metadata": {}, + "source": [ + "(Notice the absence of for loops --- every operation is vectorized, meaning that the major calculations are all shifted to optimized C code.)\n", + "\n", + "The fit to the normal density is already tight and can be further improved by increasing `n`." + ] + }, + { + "cell_type": "markdown", + "id": "7229ffd3", + "metadata": {}, + "source": [ + "## Exercises" + ] + }, + { + "cell_type": "markdown", + "id": "b49befe8", + "metadata": {}, + "source": [ + "## Ex 1" + ] + }, + { + "cell_type": "markdown", + "id": "57710f7b", + "metadata": {}, + "source": [ + "As the reader to rerun the last simulation and experiment with other specifications of $F$ that have finite second moment, making sure that they" + ] + }, + { + "cell_type": "markdown", + "id": "2ed84c17", + "metadata": {}, + "source": [ + "Although NumPy doesn't give us a `bernoulli` function, we can generate a draw of $X$ using NumPy via" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "1b300696", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1\n" + ] + } + ], + "source": [ + "U = np.random.rand()\n", + "X = 1 if U < p else 0\n", + "print(X)" + ] + }, + { + "cell_type": "markdown", + "id": "dcd111f0", + "metadata": {}, + "source": [ + "Explain why this provides a random variable $X$ with the right distribution." + ] + }, + { + "cell_type": "markdown", + "id": "c7564cf9", + "metadata": {}, + "source": [ + "Solution:" + ] + }, + { + "cell_type": "markdown", + "id": "2fa6cb25", + "metadata": {}, + "source": [ + "We can write $X$ as $X = \\mathbf 1\\{U < p\\}$ where $\\mathbf 1$ is the [indicator function](https://en.wikipedia.org/wiki/Indicator_function) (i.e., 1 if the statement is true and zero otherwise).\n", + "\n", + "Here we generated a uniform draw $U$ on $[0,1]$ and then used the fact that\n", + "\n", + "$$\n", + "\\mathbb P\\{0 \\leq U < p\\} = p - 0 = p\n", + "$$\n", + "\n", + "This means that $X = \\mathbf 1\\{U < p\\}$ has the right distribution." + ] + }, + { + "cell_type": "markdown", + "id": "00e14b9a", + "metadata": {}, + "source": [ + "```{solution-end}\n", + "```" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.15" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From 0c3f535e08df92a10b3f40f8e86bb690b7ed6641 Mon Sep 17 00:00:00 2001 From: Humphrey Yang Date: Tue, 31 Jan 2023 09:42:10 +1100 Subject: [PATCH 02/12] minor changes --- in-work/lln_clt.ipynb | 55 ++++++++++++++++++++++++++----------------- 1 file changed, 33 insertions(+), 22 deletions(-) diff --git a/in-work/lln_clt.ipynb b/in-work/lln_clt.ipynb index 566c8435c..341c6933f 100644 --- a/in-work/lln_clt.ipynb +++ b/in-work/lln_clt.ipynb @@ -124,7 +124,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "0.79964\n" + "0.800089\n" ] } ], @@ -152,7 +152,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "0.300404\n" + "0.30005\n" ] } ], @@ -295,7 +295,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 23, "id": "9299240a", "metadata": {}, "outputs": [], @@ -312,14 +312,14 @@ " return np.mean(X_samples)\n", " \n", " # Step 5: Loop m times\n", - " sample_means = np.array([draw_means(distribution, n) for i in range(m)])\n", + " sample_means = [draw_means(distribution, n) for i in range(m)]\n", " print(f'The mean of sample mean is {round(np.mean(sample_means),2)}')\n", " \n", " # Generate a histogram\n", " ax.hist(sample_means, bins=30, alpha=0.5, density=True)\n", " mu = X_distribution.mean()\n", " if not np.isnan(mu):\n", - " ax.axvline(x=5, ls=\"--\", lw=3, label=fr\"$\\mu = {mu}$\")\n", + " ax.axvline(x=mu, ls=\"--\", lw=3, label=fr\"$\\mu = {mu}$\")\n", " \n", " ax.set_xlim(min(sample_means), max(sample_means))\n", " ax.set_xlabel(r'$\\bar x$')\n", @@ -331,7 +331,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 24, "id": "c3056496-bc32-45ca-b733-53a1a990692a", "metadata": {}, "outputs": [ @@ -344,7 +344,7 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -431,7 +431,7 @@ " \n", " mu = X_distribution.mean()\n", " if not np.isnan(mu):\n", - " ax.axvline(x=5, ls=\"--\", lw=3, label=fr\"$\\mu = {mu}$\")\n", + " ax.axvline(x=mu, ls=\"--\", lw=3, label=fr\"$\\mu = {mu}$\")\n", " \n", " ax.set_xlim(min(sample_means), max(sample_means)) \n", " ax.set_xlabel(r'$\\bar x$')\n", @@ -449,7 +449,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -489,7 +489,7 @@ "outputs": [ { "data": { - "image/png": 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" ] @@ -514,13 +514,13 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 11, "id": "dda56a48-d06c-4ed4-9c7e-180d843d1d63", "metadata": {}, "outputs": [ { "data": { - "image/png": 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"text/plain": [ "
" ] @@ -541,9 +541,11 @@ " ax.scatter(range(burn_in, n+1, jump), sample_means, s=10)\n", " if ylog:\n", " ax.set_yscale(\"symlog\")\n", - " ax.set_title(title)\n", + " ax.set_title(title, size=10)\n", " ax.set_xlabel(\"Sample Size\")\n", " ax.set_ylabel(\"Sample Mean\")\n", + " yabs_max = max(ax.get_ylim(), key=abs)\n", + " ax.set_ylim(ymin=-yabs_max, ymax=yabs_max)\n", " return ax\n", "\n", "scattered_mean(distribution=st.cauchy(), \n", @@ -585,7 +587,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -603,6 +605,7 @@ " _, ax = plt.subplots(figsize=(10, 6))\n", "\n", " for i in range(n):\n", + " # Dependency\n", " if samples[i] > 5:\n", " samples[i+1] = st.norm.rvs(loc=5, scale=2, size=1)\n", " else:\n", @@ -610,13 +613,13 @@ "\n", " # Plot the stock prices without iid assumption\n", " ax.hist(samples, label=\"non-iid\", bins=60, alpha=0.5, density=True)\n", - " distribution = st.norm\n", - " ax.hist(distribution.rvs(loc=5, scale=2, size=n), bins=60, label=\"iid\", alpha=0.5, density=True)\n", + " distribution = st.norm(loc=5, scale=2)\n", + " ax.hist(distribution.rvs(size=n), bins=60, label=\"iid\", alpha=0.5, density=True)\n", "\n", " # Add labels and legend\n", " ax.set_xlabel(r'$\\bar x$')\n", " ax.set_ylabel('Density')\n", - " ax.axvline(x=5, ls=\"--\", lw=3, label=fr\"$\\mu = {distribution.mean()}$\")\n", + " ax.axvline(x=distribution.mean(), ls=\"--\", lw=3, label=fr\"$\\mu = {distribution.mean()}$\")\n", " ax.legend()\n", "\n", " # Show the plot\n", @@ -625,6 +628,14 @@ "iid_comparison(n, 0.9)" ] }, + { + "cell_type": "markdown", + "id": "c435af34-8366-410b-b4d8-793665d8dd0b", + "metadata": {}, + "source": [ + "In this case, since the samples are neither drawn independently nor identically distributed, and the converging trend towards $\\mu$ is not found." + ] + }, { "cell_type": "markdown", "id": "59934170", @@ -701,7 +712,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -715,7 +726,7 @@ "n = 250 # Choice of n\n", "k = 1_000_000 # Number of draws of Y_n\n", "distribution = st.expon(2) # Exponential distribution, λ = 1/2\n", - "μ, s = distribution.mean(), distribution.std()\n", + "μ, σ = distribution.mean(), distribution.std()\n", "\n", "# Draw underlying RVs. Each row contains a draw of X_1,..,X_n\n", "data = distribution.rvs((k, n))\n", @@ -726,11 +737,11 @@ "\n", "# Plot\n", "fig, ax = plt.subplots(figsize=(10, 6))\n", - "xmin, xmax = -3 * s, 3 * s\n", + "xmin, xmax = -3 * σ, 3 * σ\n", "ax.set_xlim(xmin, xmax)\n", "ax.hist(Y, bins=60, alpha=0.4, density=True)\n", "xgrid = np.linspace(xmin, xmax, 200)\n", - "ax.plot(xgrid, st.norm.pdf(xgrid, scale=s), 'k-', lw=2, label='$N(0, \\sigma^2)$')\n", + "ax.plot(xgrid, st.norm.pdf(xgrid, scale=σ), 'k-', lw=2, label='$N(0, \\sigma^2)$')\n", "ax.legend()\n", "\n", "plt.show()" From ddb41b3c23b492cc8f411e79ec8600a9623ee940 Mon Sep 17 00:00:00 2001 From: Humphrey Yang Date: Tue, 31 Jan 2023 14:37:40 +1100 Subject: [PATCH 03/12] update lln_clt for review --- in-work/lln_clt.ipynb | 290 ++++++++++++++++-------------------------- in-work/lln_clt.md | 262 +++++++++++++++++++++++++++++++------- 2 files changed, 331 insertions(+), 221 deletions(-) diff --git a/in-work/lln_clt.ipynb b/in-work/lln_clt.ipynb index 341c6933f..70598c5c6 100644 --- a/in-work/lln_clt.ipynb +++ b/in-work/lln_clt.ipynb @@ -94,7 +94,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "1\n" + "0\n" ] } ], @@ -124,7 +124,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "0.800089\n" + "0.800251\n" ] } ], @@ -152,7 +152,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "0.30005\n" + "0.299723\n" ] } ], @@ -290,12 +290,16 @@ "\n", "Moreover, if we repeat the exercise with a larger value of $n$, we should see that the observations are even more tightly clustered around the population mean.\n", "\n", - "This is, in essence, what the LLN is telling us." + "This is, in essence, what the LLN is telling us.\n", + "\n", + "Let's run some simulations to visualize LLN\n", + "\n", + "Let's" ] }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 11, "id": "9299240a", "metadata": {}, "outputs": [], @@ -306,13 +310,13 @@ " def draw_means(X_distribution, n):\n", "\n", " # Step 3: Generate n draws: X_1, ..., X_n\n", - " X_samples = distribution.rvs(size=n)\n", + " X_samples = X_distribution.rvs(size=n)\n", "\n", " # Step 4: Calculate sample mean\n", " return np.mean(X_samples)\n", " \n", " # Step 5: Loop m times\n", - " sample_means = [draw_means(distribution, n) for i in range(m)]\n", + " sample_means = [draw_means(X_distribution, n) for i in range(m)]\n", " print(f'The mean of sample mean is {round(np.mean(sample_means),2)}')\n", " \n", " # Generate a histogram\n", @@ -324,56 +328,13 @@ " ax.set_xlim(min(sample_means), max(sample_means))\n", " ax.set_xlabel(r'$\\bar x$')\n", " ax.set_ylabel('Density')\n", - " ax.set(title=fr'$n = {n}, m = {m}$')\n", " ax.legend()\n", " plt.show()" ] }, { "cell_type": "code", - "execution_count": 24, - "id": "c3056496-bc32-45ca-b733-53a1a990692a", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The mean of sample mean is 5.0\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Step 1: Draw from a normal distribution\n", - "distribution = st.norm(loc=5, scale=2)\n", - "\n", - "# Step 2: Set n to some large number and generate samples and set m to a large number for iterations\n", - "generate_histogram(distribution, n=1000, m=1000)" - ] - }, - { - "cell_type": "markdown", - "id": "baedeccf-e5d5-432c-8bd6-5e02684c956a", - "metadata": {}, - "source": [ - "We can see that the distribution of $\\bar X$ is clustered around $\\mathbb E X$ as expected.\n", - "\n", - "We can increase values for `n` and `m` to see how the distribution changes" - ] - }, - { - "cell_type": "code", - "execution_count": 7, + "execution_count": 14, "id": "0b0da74f-1f3d-4b75-bb4a-86c85c4539bb", "metadata": {}, "outputs": [ @@ -386,7 +347,7 @@ }, { "data": { - "image/png": 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gBAAAkGLVOwCgRTZtboh/eXJlVtuUY/aP7l2LClQRQO4ISgBAiySRxKYtDc3aADoCl94BAACkCEoAAAApghIAAECKoAQAAJAiKAEAAKQISgAAACmCEgAAQIqgBAAAkCIoAQAApAhKAAAAKQUNStXV1ZHJZLK2ioqKpv1JkkR1dXVUVVVF9+7dY+zYsbF06dICVgwAAHQGBZ9ROuKII2L16tVN23PPPde075prromZM2fG9ddfHwsWLIiKiooYP358rF+/voAVAwAAHV3Bg1JxcXFUVFQ0bfvss09EfDibdN1118Wll14ap512WgwZMiRmzZoVGzdujDvvvLPAVQMAAB1ZwYPSyy+/HFVVVTFw4MA444wz4rXXXouIiOXLl0dtbW1MmDChqW9paWmMGTMm5s+fv8Pj1dfXx7p167I2ACD3Soq6xMiBfbK2kqKCf7QAyIniQr74yJEj44477oiDDz443nrrrbjyyitj9OjRsXTp0qitrY2IiPLy8qznlJeXx8qVK3d4zBkzZsTll1+e17oBgA+D0jGD+ha6DIC8KOjXPhMnTowvfelLMXTo0Bg3blw88MADERExa9aspj6ZTCbrOUmSNGv7qEsuuSTWrl3btK1atSo/xQMAAB1Wm5of32OPPWLo0KHx8ssvN61+t21maZu6urpms0wfVVpaGr169craAAAAdkWbCkr19fXxwgsvRGVlZQwcODAqKipi7ty5Tfs3b94c8+bNi9GjRxewSgAAoKMr6D1KF154YXzhC1+IAQMGRF1dXVx55ZWxbt26OPPMMyOTycTUqVOjpqYmBg8eHIMHD46ampro0aNHTJ48uZBlAwAAHVxBg9Ibb7wRX/3qV+Ptt9+OffbZJ4455ph48sknY//994+IiIsuuig2bdoU5513XqxZsyZGjhwZc+bMibKyskKWDQAAdHCZJEmSQheRT+vWrYvevXvH2rVr3a8EALvo2rkv7XDfB1sa4u6Fb2S1/e3w/aJbSdEuv8608Qfv8nMAdtWuZIOCzigBAO1XY5LEu+9vbtYG0BG0qcUcAAAA2gJBCQAAIEVQAgAASBGUAAAAUgQlAACAFEEJAAAgRVACAABIEZQAAABSBCUAAIAUQQkAACBFUAIAAEgRlAAAAFIEJQAAgJTiQhcAALRPxV26xLB9ezdrA+gIBCUAoEW6FneJEw7tV+gyAPLC1z4AAAApghIAAECKoAQAAJAiKAEAAKQISgAAAClWvQMAWqR+S0P8x7Ors9q+MKwySkuKClQRQO4ISgBAizQkSbz53qZmbQAdgUvvAAAAUgQlAACAFEEJAAAgRVACAABIEZQAAABSBCUAAIAUQQkAACBFUAIAAEgRlAAAAFIEJQAAgBRBCQAAIEVQAgAASBGUAAAAUooLXQAA0D4VdcnEQf16NmsD6AgEJQCgRUqLi+KUoZWFLgMgL1x6BwAAkCIoAQAApAhKAAAAKYISAABAiqAEAACQYtU7AKBF6rc2xH+9UJfVNu6wflFaXFSgigByR1ACAFqkoTGJV+o2ZLWdcMg+BaoGILdcegcAAJAiKAEAAKQISgAAACmCEgAAQIqgBAAAkCIoAQAApAhKAAAAKYISAABAiqAEAACQIigBAACkCEoAAAApghIAAECKoAQAAJBSXOgCAID2qSiTiX337N6sDaAjEJQAgBYpLSmKLw/fr9BlAOSFS+8AAABSBCUAAIAUQQkAACBFUAIAAEgRlAAAAFKsegcAtMjmrY3xx1fezmo79qC9o2ux72GB9k9QAgBaZGtjYzz75tqstpGD+kRXF6wAHYCgBADt0LVzXyp0CQAdWpv5ymfGjBmRyWRi6tSpTW1JkkR1dXVUVVVF9+7dY+zYsbF06dLCFQkAAHQKbSIoLViwIG6++eYYNmxYVvs111wTM2fOjOuvvz4WLFgQFRUVMX78+Fi/fn2BKgUAADqDggelDRs2xNe+9rW45ZZbYq+99mpqT5Ikrrvuurj00kvjtNNOiyFDhsSsWbNi48aNceeddxawYgAAoKMreFA6//zz45RTTolx48ZltS9fvjxqa2tjwoQJTW2lpaUxZsyYmD9//g6PV19fH+vWrcvaAAAAdkVBF3O46667YtGiRbFgwYJm+2prayMiory8PKu9vLw8Vq5cucNjzpgxIy6//PLcFgoAAHQqBZtRWrVqVVxwwQXxq1/9Krp167bDfplMJutxkiTN2j7qkksuibVr1zZtq1atylnNAABA51CwGaWFCxdGXV1dDB8+vKmtoaEhHnvssbj++utj2bJlEfHhzFJlZWVTn7q6umazTB9VWloapaWl+SscAADo8Ao2o/S5z30unnvuuViyZEnTNmLEiPja174WS5YsiUGDBkVFRUXMnTu36TmbN2+OefPmxejRowtVNgAA0AkUbEaprKwshgwZktW2xx57RN++fZvap06dGjU1NTF48OAYPHhw1NTURI8ePWLy5MmFKBkAAOgkCrqYwye56KKLYtOmTXHeeefFmjVrYuTIkTFnzpwoKysrdGkAQA5dO/elVnmdaeMPbpXXAdq/NhWUHn300azHmUwmqquro7q6uiD1AAAAnVPBf0cJAACgrWlTM0oA0N611iVkbUGXTCb67NG1WVtb5hI/YGcJSgBAi3QrKYopx+xf6DIA8sKldwAAACmCEgAAQIqgBAAAkCIoAQAApAhKAAAAKVa9AwBaZEtDYyxcuSarbfj+e0VJke9hgfZPUAIAWmRLQ2P8afm7WW3D9ustKAEdgr9kAAAAKYISAABAiqAEAACQIigBAACkCEoAAAApghIAAECKoAQAAJAiKAEAAKQISgAAACmCEgAAQIqgBAAAkCIoAQAApAhKAAAAKcWFLgAAaJ8ykYnuJUXN2gA6AkEJAGiR7l2L4n9+dlChywDIC5feAQAApAhKAAAAKYISAABAiqAEAACQIigBAACkWPUOAGiRrQ2NsfQv67LajqjqFcVFvocF2j9BCQBokc0NjfHoS3/Nahtc3lNQAjoEf8kAAABSBCUAAIAUQQkAACBFUAIAAEgRlAAAAFIEJQAAgBRBCQAAIEVQAgAASBGUAAAAUgQlAACAFEEJAAAgRVACAABIKS50AQDQWq6d+1KhSwCgnTCjBAAAkGJGCQBokR5di+OCzw0udBkAeWFGCQAAIEVQAgAASBGUAAAAUgQlAACAFEEJAAAgxap3AECLbG1sjOV/fT+rbeA+e0RxF9/DAu2foAQAtMjmrY3x4J9rs9q+dfzAKO4qKAHtn79kAAAAKYISAABAiqAEAACQ0qKgtHz58lzXAQAA0Ga0KCgddNBBccIJJ8SvfvWr+OCDD3JdEwAAQEG1KCg988wzcfTRR8ff//3fR0VFRZx77rnx1FNP5bo2AACAgmhRUBoyZEjMnDkz3nzzzbjtttuitrY2jjvuuDjiiCNi5syZ8de//jXXdQIAALSa3VrMobi4OE499dT4t3/7t/jxj38cr776alx44YWx3377xTe+8Y1YvXp1ruoEAABoNbsVlJ5++uk477zzorKyMmbOnBkXXnhhvPrqq/GHP/wh3nzzzZg0aVKu6gQAAGg1xS150syZM+O2226LZcuWxcknnxx33HFHnHzyydGly4e5a+DAgfGLX/wiDj300JwWCwAA0BpaFJRuuumm+OY3vxlnn312VFRUbLfPgAED4tZbb92t4gAAAAqhRUFp7ty5MWDAgKYZpG2SJIlVq1bFgAEDomvXrnHmmWfmpEgAAIDW1KJ7lA488MB4++23m7W/++67MXDgwN0uCgAAoJBaFJSSJNlu+4YNG6Jbt267VRAAAECh7dKld9OnT4+IiEwmEz/84Q+jR48eTfsaGhriT3/6Uxx11FE5LRAAaJu6lxTFt44f2KwNoCPYpRmlxYsXx+LFiyNJknjuueeaHi9evDhefPHFOPLII+P222/f6ePddNNNMWzYsOjVq1f06tUrRo0aFb/73e+a9idJEtXV1VFVVRXdu3ePsWPHxtKlS3elZAAgTzKZTPToWpy1ZTKZQpcFkBO7NKP0yCOPRETE2WefHT/72c+iV69eu/Xi++23X1x99dVx0EEHRUTErFmzYtKkSbF48eI44ogj4pprromZM2fG7bffHgcffHBceeWVMX78+Fi2bFmUlZXt1msDAADsSCbZ0Q1HBdKnT5/4yU9+Et/85jejqqoqpk6dGv/wD/8QERH19fVRXl4eP/7xj+Pcc8/dqeOtW7cuevfuHWvXrt3tYAdA+3bt3JcKXQKdxLTxBxe6BGA7diUb7PSM0mmnnRa333579OrVK0477bSP7Xvfffft7GGbNDQ0xN133x3vv/9+jBo1KpYvXx61tbUxYcKEpj6lpaUxZsyYmD9//g6DUn19fdTX1zc9Xrdu3S7XAgAAdG47HZR69+7ddN1x7969c1bAc889F6NGjYoPPvggevbsGffff38cfvjhMX/+/IiIKC8vz+pfXl4eK1eu3OHxZsyYEZdffnnO6gMAADqfnQ5Kt91223b/vbsOOeSQWLJkSbz33ntx7733xplnnhnz5s1r2p++KTRJko+9UfSSSy5pWp0v4sMZpf79++esXgDgQw2NSaxeuymrrbJ39yjqYkEHoP3bpcUcttm0aVMkSdK0PPjKlSubZoI+eqnczujatWvTYg4jRoyIBQsWxM9+9rOm+5Jqa2ujsrKyqX9dXV2zWaaPKi0tjdLS0l09JQBgF9VvbYh7F72Z1fat4wdGj64t+ngB0Ka06AdnJ02aFHfccUdERLz33nvxmc98Jn7605/GpEmT4qabbtqtgpIkifr6+hg4cGBUVFTE3Llzm/Zt3rw55s2bF6NHj96t1wAAAPg4LQpKixYtiuOPPz4iIu65556oqKiIlStXxh133BH/9E//tNPH+d73vhePP/54rFixIp577rm49NJL49FHH42vfe1rkclkYurUqVFTUxP3339//PnPf46zzjorevToEZMnT25J2QAAADulRXPjGzdubPodozlz5sRpp50WXbp0iWOOOeZjF1pIe+utt2LKlCmxevXq6N27dwwbNiweeuihGD9+fEREXHTRRbFp06Y477zzYs2aNTFy5MiYM2eO31ACAADyqkVB6aCDDorf/OY3ceqpp8bDDz8c06ZNi4gP7x/ald8quvXWWz92fyaTierq6qiurm5JmQAAAC3SokvvfvjDH8aFF14YBxxwQIwcOTJGjRoVER/OLh199NE5LRAAAKC1tWhG6ctf/nIcd9xxsXr16jjyyCOb2j/3uc/FqaeemrPiAAAACqHF63dWVFRERUVFVttnPvOZ3S4IAACg0FoUlN5///24+uqr4/e//33U1dVFY2Nj1v7XXnstJ8UBAAAUQouC0jnnnBPz5s2LKVOmRGVlZWQyfoEbAADoOFoUlH73u9/FAw88EMcee2yu6wEAACi4Fq16t9dee0WfPn1yXQsAAECb0KKg9KMf/Sh++MMfxsaNG3NdDwAAQMG16NK7n/70p/Hqq69GeXl5HHDAAVFSUpK1f9GiRTkpDgAAoBBaFJS++MUv5rgMAACAtqNFQemyyy7LdR0AQDvTrbgovj5yQLM2gI6gxT84+95778U999wTr776avyf//N/ok+fPrFo0aIoLy+PfffdN5c1AgBtUJcumejbs7TQZQDkRYuC0rPPPhvjxo2L3r17x4oVK+Jb3/pW9OnTJ+6///5YuXJl3HHHHbmuEwAAoNW0KChNnz49zjrrrLjmmmuirKysqX3ixIkxefLknBUHANAeXTv3pby/xrTxB+f9NaAza9Hy4AsWLIhzzz23Wfu+++4btbW1u10UAABAIbUoKHXr1i3WrVvXrH3ZsmWxzz777HZRAAAAhdSioDRp0qS44oorYsuWLRERkclk4vXXX4+LL744vvSlL+W0QACgbWpsTOKdDfVZW2NjUuiyAHKiRfco/eM//mOcfPLJ0a9fv9i0aVOMGTMmamtrY9SoUXHVVVflukYAoA36YGtD/OpPr2e1fev4gdGja4sX1QVoM1r0l6xXr17xxBNPxCOPPBILFy6MxsbG+NSnPhXjxo3LdX0AAACtbpeDUmNjY9x+++1x3333xYoVKyKTycTAgQOjoqIikiSJTCaTjzoBAABazS7do5QkSfyP//E/4pxzzok333wzhg4dGkcccUSsXLkyzjrrrDj11FPzVScAAECr2aUZpdtvvz0ee+yx+P3vfx8nnHBC1r4//OEP8cUvfjHuuOOO+MY3vpHTIgEAAFrTLs0ozZ49O773ve81C0kRESeeeGJcfPHF8a//+q85Kw4AAKAQdikoPfvss/E3f/M3O9w/ceLEeOaZZ3a7KAAAgELapaD07rvvRnl5+Q73l5eXx5o1a3a7KAAAgELapaDU0NAQxcU7vq2pqKgotm7duttFAQAAFNIuLeaQJEmcddZZUVpaut399fX1OSkKAACgkHYpKJ155pmf2MeKdwAAQHu3S0Hptttuy1cdAAAAbcYu3aMEAADQGQhKAAAAKYISAABAyi7dowQAsE1pcVF86VP7NmsD6AgEJQCgRYq6ZGK/vXoUugyAvHDpHQAAQIoZJQAK7tq5LxW6BADIYkYJAAAgRVACAABIcekdANAiSZLEpi0NWW3dS4oik8kUqCKA3BGUAIAW2bSlIW55fHlW27eOHxg9uvp4AbR/Lr0DAABIEZQAAABSBCUAAIAUQQkAACBFUAIAAEgRlAAAAFIEJQAAgBRBCQAAIEVQAgAASBGUAAAAUgQlAACAFEEJAAAgRVACAABIEZQAAABSigtdAADQPnUt7hInD6lo1gbQEQhKAECLFHfpEoPLywpdBkBe+NoHAAAgRVACAABIEZQAAABSBCUAAIAUQQkAACDFqncAQIts3Lw1bnl8eVbbt44fGD26+ngBtH9mlAAAAFIEJQAAgBRBCQAAIEVQAgAASBGUAAAAUgQlAACAlIIGpRkzZsSnP/3pKCsri379+sUXv/jFWLZsWVafJEmiuro6qqqqonv37jF27NhYunRpgSoGAAA6g4IGpXnz5sX5558fTz75ZMydOze2bt0aEyZMiPfff7+pzzXXXBMzZ86M66+/PhYsWBAVFRUxfvz4WL9+fQErBwAAOrKC/iLcQw89lPX4tttui379+sXChQvjs5/9bCRJEtddd11ceumlcdppp0VExKxZs6K8vDzuvPPOOPfccwtRNgAA0MG1qXuU1q5dGxERffr0iYiI5cuXR21tbUyYMKGpT2lpaYwZMybmz5+/3WPU19fHunXrsjYAAIBd0WaCUpIkMX369DjuuONiyJAhERFRW1sbERHl5eVZfcvLy5v2pc2YMSN69+7dtPXv3z+/hQMAAB1OmwlK3/nOd+LZZ5+N2bNnN9uXyWSyHidJ0qxtm0suuSTWrl3btK1atSov9QIAAB1XQe9R2uZ//+//Hb/97W/jsccei/3226+pvaKiIiI+nFmqrKxsaq+rq2s2y7RNaWlplJaW5rdgAACgQyvojFKSJPGd73wn7rvvvvjDH/4QAwcOzNo/cODAqKioiLlz5za1bd68OebNmxejR49u7XIBAIBOoqAzSueff37ceeed8e///u9RVlbWdN9R7969o3v37pHJZGLq1KlRU1MTgwcPjsGDB0dNTU306NEjJk+eXMjSAaDT61rUJcYevE+zNoCOoKBB6aabboqIiLFjx2a133bbbXHWWWdFRMRFF10UmzZtivPOOy/WrFkTI0eOjDlz5kRZWVkrVwsAfFRxUZc4sv+ehS4DIC8KGpSSJPnEPplMJqqrq6O6ujr/BQEAAEQbWvUOAACgrRCUAAAAUgQlAACAFEEJAAAgpU384CwA0P5s2twQ//Lkyqy2KcfsH927FhWoIoDcEZQAgBZJIolNWxqatQF0BC69AwAASBGUAAAAUgQlAACAFEEJAAAgRVACAABIEZQAAABSLA8OwA5dO/elQpcA7EBr/f+cNv7gVnkdaGvMKAEAAKQISgAAACkuvQMAYIdc4kdnZUYJAAAgRVACAABIEZQAAABS3KMEALRISVGXGDmwT7M2gI5AUAIAWqSkqEscM6hvocsAyAtf+wAAAKQISgAAACmCEgAAQIqgBAAAkCIoAQAApFj1DgBokQ+2NMTdC9/Iavvb4ftFt5KiAlUEkDuCEgDQIo1JEu++v7lZG0BH4NI7AACAFEEJAAAgRVACAABIEZQAAABSBCUAAIAUQQkAACBFUAIAAEgRlAAAAFIEJQAAgBRBCQAAIEVQAgAASBGUAAAAUgQlAACAlOJCFwAAtE/FXbrEsH17N2sD6AgEJQCgRboWd4kTDu1X6DIA8sLXPgAAACmCEgAAQIqgBAAAkCIoAQAApAhKAAAAKVa9AwBapH5LQ/zHs6uz2r4wrDJKS4oKVBFA7ghKAECLNCRJvPnepmZtAB2BS+8AAABSBCUAAIAUQQkAACBFUAIAAEgRlAAAAFIEJQAAgBRBCQAAIMXvKAEAUHDXzn2pVV5n2viDW+V1aP/MKAEAAKQISgAAACmCEgAAQIqgBAAAkCIoAQAApFj1DgBokaIumTioX89mbQAdgaAE0A611jK68HFKi4vilKGVhS4DIC9cegcAAJAiKAEAAKQISgAAACkFDUqPPfZYfOELX4iqqqrIZDLxm9/8Jmt/kiRRXV0dVVVV0b179xg7dmwsXbq0MMUCAACdRkGD0vvvvx9HHnlkXH/99dvdf80118TMmTPj+uuvjwULFkRFRUWMHz8+1q9f38qVAgAAnUlBV72bOHFiTJw4cbv7kiSJ6667Li699NI47bTTIiJi1qxZUV5eHnfeeWece+65rVkqAJBSv7Uh/uuFuqy2cYf1i9LiogJVBJA7bfYepeXLl0dtbW1MmDChqa20tDTGjBkT8+fP3+Hz6uvrY926dVkbAJB7DY1JvFK3IWtraEwKXRZATrTZoFRbWxsREeXl5Vnt5eXlTfu2Z8aMGdG7d++mrX///nmtEwAA6HjabFDaJpPJ/oXvJEmatX3UJZdcEmvXrm3aVq1ale8SAQCADqag9yh9nIqKioj4cGapsvL//ep3XV1ds1mmjyotLY3S0tK81wewPdfOfanQJQAAOdBmZ5QGDhwYFRUVMXfu3Ka2zZs3x7x582L06NEFrAwAAOjoCjqjtGHDhnjllVeaHi9fvjyWLFkSffr0iQEDBsTUqVOjpqYmBg8eHIMHD46ampro0aNHTJ48uYBVAwAAHV1Bg9LTTz8dJ5xwQtPj6dOnR0TEmWeeGbfffntcdNFFsWnTpjjvvPNizZo1MXLkyJgzZ06UlZUVqmQAAKATKGhQGjt2bCTJjpcRzWQyUV1dHdXV1a1XFAAA0Om12XuUAAAACkVQAgAASBGUAAAAUgQlAACAFEEJAAAgRVACAABIKejy4ABA+1WUycS+e3Zv1gbQEQhKAECLlJYUxZeH71foMgDywqV3AAAAKYISAABAiqAEAACQIigBAACkCEoAAAApVr0DAFpk89bG+OMrb2e1HXvQ3tG12PewQPsnKAEALbK1sTGefXNtVtvIQX2iqwtWIK6d+1KrvM608Qe3yut0Rv6SAQAApAhKAAAAKYISAABAiqAEAACQIigBAACkCEoAAAAplgcHOoXWWqYVAOgYzCgBAACkCEoAAAApghIAAECKoAQAAJAiKAEAAKQISgAAACmWBwcAWqRLJhN99ujarA2gIxCUAIAW6VZSFFOO2b/QZQDkhUvvAAAAUgQlAACAFEEJAAAgRVACAABIEZQAAABSrHoHALTIlobGWLhyTVbb8P33ipIi38MC7Z+gBAC0yJaGxvjT8nez2obt11tQAjoEf8kAAABSBCUAAIAUQQkAACBFUAIAAEgRlAAAAFIEJQAAgBRBCQAAIMXvKAEA0GlcO/elQpdAO2FGCQAAIEVQAgAASBGUAAAAUgQlAACAFEEJAAAgxap3AECLZCIT3UuKmrUBrac1VvGbNv7gvL9GWyQoAQAt0r1rUfzPzw4qdBkAeeHSOwAAgBRBCQAAIEVQAgAASBGUAAAAUgQlAACAFKveAQXXGkubArm3taExlv5lXVbbEVW9orjI97BA+ycoAQAtsrmhMR596a9ZbYPLewpKQIfgLxkAAECKoAQAAJAiKAEAAKQISgAAACkWcwB2yGp0AEBnZUYJAAAgRVACAABIcekdAACwQ611Kf608Qe3yuvsLDNKAAAAKYISAABASrsISjfeeGMMHDgwunXrFsOHD4/HH3+80CUBAAAdWJu/R+nXv/51TJ06NW688cY49thj4xe/+EVMnDgxnn/++RgwYMBOH+eGP7wS3fbomcdK2951lXRclu0GADqa1vh888H7G3a6b5ufUZo5c2b83d/9XZxzzjlx2GGHxXXXXRf9+/ePm266qdClAQAAHVSbnlHavHlzLFy4MC6++OKs9gkTJsT8+fO3+5z6+vqor69verx27dqIiPhg486nx5Zat25d3l8DInbt2xCAfPlgy9ZorN+Y3bZxQ3TZ0qY/XgCd2LZMkCTJJ/Zt03/J3n777WhoaIjy8vKs9vLy8qitrd3uc2bMmBGXX355s/YrvjYmLzV+1Pfy/goA0LZdeV2hKwD4ZOvXr4/evXt/bJ82HZS2yWQyWY+TJGnWts0ll1wS06dPb3rc2NgY7777bvTt23eHz2kv1q1bF/37949Vq1ZFr169Cl0OO2Cc2gfj1D4Yp/bBOLUPxql9ME75lSRJrF+/Pqqqqj6xb5sOSnvvvXcUFRU1mz2qq6trNsu0TWlpaZSWlma17bnnnvkqsSB69erlP047YJzaB+PUPhin9sE4tQ/GqX0wTvnzSTNJ27TpxRy6du0aw4cPj7lz52a1z507N0aPHl2gqgAAgI6uTc8oRURMnz49pkyZEiNGjIhRo0bFzTffHK+//np8+9vfLnRpAABAB9Xmg9Lpp58e77zzTlxxxRWxevXqGDJkSDz44IOx//77F7q0VldaWhqXXXZZs0sLaVuMU/tgnNoH49Q+GKf2wTi1D8ap7cgkO7M2HgAAQCfSpu9RAgAAKARBCQAAIEVQAgAASBGUAAAAUgSlNmDGjBmRyWRi6tSpH9vvhhtuiMMOOyy6d+8ehxxySNxxxx3N+rz33ntx/vnnR2VlZXTr1i0OO+ywePDBB/NUeeeSq3EaO3ZsZDKZZtspp5ySx+o7j1z+f7ruuuvikEMOie7du0f//v1j2rRp8cEHH+Sp8s4lV+O0ZcuWuOKKK+LAAw+Mbt26xZFHHhkPPfRQHivv+Kqrq5v9faqoqPjY58ybNy+GDx8e3bp1i0GDBsXPf/7zZn3uvffeOPzww6O0tDQOP/zwuP/++/N1Cp1CPsZp6dKl8aUvfSkOOOCAyGQycd111+XxDDqHfIzTLbfcEscff3zstddesddee8W4cePiqaeeyudpdF4JBfXUU08lBxxwQDJs2LDkggsu2GG/G2+8MSkrK0vuuuuu5NVXX01mz56d9OzZM/ntb3/b1Ke+vj4ZMWJEcvLJJydPPPFEsmLFiuTxxx9PlixZ0gpn0rHlcpzeeeedZPXq1U3bn//856SoqCi57bbb8n8iHVwux+lXv/pVUlpamvzrv/5rsnz58uThhx9OKisrk6lTp7bCmXRsuRyniy66KKmqqkoeeOCB5NVXX01uvPHGpFu3bsmiRYta4Uw6pssuuyw54ogjsv5O1dXV7bD/a6+9lvTo0SO54IILkueffz655ZZbkpKSkuSee+5p6jN//vykqKgoqampSV544YWkpqYmKS4uTp588snWOKUOKR/j9NRTTyUXXnhhMnv27KSioiK59tprW+FMOrZ8jNPkyZOTG264IVm8eHHywgsvJGeffXbSu3fv5I033miNU+pUBKUCWr9+fTJ48OBk7ty5yZgxYz72A8OoUaOSCy+8MKvtggsuSI499timxzfddFMyaNCgZPPmzfkquVPK9TilXXvttUlZWVmyYcOGXJXcKeV6nM4///zkxBNPzOozffr05Ljjjstp3Z1NrsepsrIyuf7667P6TJo0Kfna176W07o7k8suuyw58sgjd7r/RRddlBx66KFZbeeee25yzDHHND3+yle+kvzN3/xNVp+TTjopOeOMM3ar1s4sH+P0Ufvvv7+glAP5HqckSZKtW7cmZWVlyaxZs1paJjvg0rsCOv/88+OUU06JcePGfWLf+vr66NatW1Zb9+7d46mnnootW7ZERMRvf/vbGDVqVJx//vlRXl4eQ4YMiZqammhoaMhL/Z1Frscp7dZbb40zzjgj9thjj5zU21nlepyOO+64WLhwYdPlDK+99lo8+OCDLpHcTbkepx31eeKJJ3JXdCf08ssvR1VVVQwcODDOOOOMeO2113bY97//+79jwoQJWW0nnXRSPP30003jtKM+8+fPz33xnUiux4n8yPc4bdy4MbZs2RJ9+vTJad24R6lg7rrrrli0aFHMmDFjp/qfdNJJ8ctf/jIWLlwYSZLE008/Hf/8z/8cW7ZsibfffjsiPvwgd88990RDQ0M8+OCD8f3vfz9++tOfxlVXXZXPU+nQ8jFOH/XUU0/Fn//85zjnnHNyXXqnko9xOuOMM+JHP/pRHHfccVFSUhIHHnhgnHDCCXHxxRfn81Q6tHyM00knnRQzZ86Ml19+ORobG2Pu3Lnx7//+77F69ep8nkqHNnLkyLjjjjvi4YcfjltuuSVqa2tj9OjR8c4772y3f21tbZSXl2e1lZeXx9atW5vGaUd9amtr83MSnUA+xonca41xuvjii2PffffdqS+g2DXFhS6gM1q1alVccMEFMWfOnGbfhO7ID37wg6itrY1jjjkmkiSJ8vLyOOuss+Kaa66JoqKiiIhobGyMfv36xc033xxFRUUxfPjw+Mtf/hI/+clP4oc//GE+T6lDytc4fdStt94aQ4YMic985jO5Lr/TyNc4Pfroo3HVVVfFjTfeGCNHjoxXXnklLrjggqisrIwf/OAH+TylDilf4/Szn/0svvWtb8Whhx4amUwmDjzwwDj77LPjtttuy+fpdGgTJ05s+vfQoUNj1KhRceCBB8asWbNi+vTp231OJpPJepwkSbP27fVJt7Hz8jVO5Fa+x+maa66J2bNnx6OPPrrTf1vZeWaUCmDhwoVRV1cXw4cPj+Li4iguLo558+bFP/3TP0VxcfF2L5Xr3r17/PM//3Ns3LgxVqxYEa+//noccMABUVZWFnvvvXdERFRWVsbBBx+c9YH8sMMOi9ra2ti8eXOrnV9Hka9x2mbjxo1x1113mU3aTfkapx/84AcxZcqUOOecc2Lo0KFx6qmnRk1NTcyYMSMaGxtb+zTbvXyN0z777BO/+c1v4v3334+VK1fGiy++GD179oyBAwe29il2WHvssUcMHTo0Xn755e3ur6ioaDYzVFdXF8XFxdG3b9+P7ZP+5pyWy8U4kX+5HKd//Md/jJqampgzZ04MGzYsbzV3ZmaUCuBzn/tcPPfcc1ltZ599dhx66KHxD//wD9udedimpKQk9ttvv4j48DKWz3/+89Gly4d599hjj40777wzGhsbm9peeumlqKysjK5du+bpbDqufI3TNv/2b/8W9fX18fWvfz33xXci+RqnjRs3NhuzoqKiSD5cBCfHZ9Hx5fv/U7du3WLfffeNLVu2xL333htf+cpXcn8SnVR9fX288MILcfzxx293/6hRo+I//uM/strmzJkTI0aMiJKSkqY+c+fOjWnTpmX1GT16dP4K72RyMU7kX67G6Sc/+UlceeWV8fDDD8eIESPyWnOnVogVJGguvfrTxRdfnEyZMqXp8bJly5J/+Zd/SV566aXkT3/6U3L66acnffr0SZYvX97U5/XXX0969uyZfOc730mWLVuW/Od//mfSr1+/5Morr2zFM+nYcjFO2xx33HHJ6aef3gpVdz65GKfLLrssKSsrS2bPnp289tpryZw5c5IDDzww+cpXvtKKZ9Kx5WKcnnzyyeTee+9NXn311eSxxx5LTjzxxGTgwIHJmjVrWu9EOpi///u/Tx599NHktddeS5588snk85//fFJWVpasWLEiSZLm47RtOeNp06Ylzz//fHLrrbc2W874j3/8Y1JUVJRcffXVyQsvvJBcffXVlgffTfkYp/r6+mTx4sXJ4sWLk8rKyuTCCy9MFi9enLz88sutfn4dRT7G6cc//nHStWvX5J577sladnz9+vWtfn4dnaDURqQ/MJx55pnJmDFjmh4///zzyVFHHZV079496dWrVzJp0qTkxRdfbHac+fPnJyNHjkxKS0uTQYMGJVdddVWydevWVjiDziFX47Rs2bIkIpI5c+a0QtWdTy7GacuWLUl1dXVy4IEHJt26dUv69++fnHfeeT6A51AuxunRRx9NDjvssKS0tDTp27dvMmXKlOTNN99spTPomE4//fSksrIyKSkpSaqqqpLTTjstWbp0adP+9DglyYfjcPTRRyddu3ZNDjjggOSmm25qdty77747OeSQQ5KSkpLk0EMPTe699958n0qHlo9xWr58eRIRzbb0cdh5+Rin/ffff7vjdNlll7XCGXUumSRxDQkAAMBHWcwBAAAgRVACAABIEZQAAABSBCUAAIAUQQkAACBFUAIAAEgRlAAAAFIEJQA6vJqamujZs2fTVlNTU+iSAGjj/OAsAB3eu+++G++++27T4z59+kSfPn0KWBEAbZ2gBAAAkOLSOwA6rNmzZ0e3bt3izTffbGo755xzYtiwYbF27doCVgZAW2dGCYAOK0mSOOqoo+L444+P66+/Pi6//PL45S9/GU8++WTsu+++hS4PgDasuNAFAEC+ZDKZuOqqq+LLX/5yVFVVxc9+9rN4/PHHhSQAPpEZJQA6vE996lOxdOnSmDNnTowZM6bQ5QDQDrhHCYAO7eGHH44XX3wxGhoaory8vNDlANBOmFECoMNatGhRjB07Nm644Ya46667okePHnH33XcXuiwA2gH3KAHQIa1YsSJOOeWUuPjii2PKlClx+OGHx6c//elYuHBhDB8+vNDlAdDGmVECoMN5991349hjj43Pfvaz8Ytf/KKpfdKkSVFfXx8PPfRQAasDoD0QlAAAAFIs5gAAAJAiKAEAAKQISgAAACmCEgAAQIqgBAAAkCIoAQAApAhKAAAAKYISAABAiqAEAACQIigBAACkCEoAAAApghIAAECKoAQAAJDy/wGx2aSTAf8kkwAAAABJRU5ErkJggg==\n", + "image/png": 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\n", 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" ] @@ -396,22 +357,24 @@ } ], "source": [ - "generate_histogram(distribution, n=50_000, m=1000)" + "#Step 1: Pick some distribution to draw each $X_i$ from \n", + "#Step 2: Set $n$ to some large number\n", + "generate_histogram(st.norm(loc=5, scale=2), n=50_000, m=1000)" ] }, { "cell_type": "markdown", - "id": "e497302a-21fd-4220-ab7f-2fdd44b7941e", + "id": "8dd3b5c4-e6b5-4df6-82e0-5b1d96e06f82", "metadata": {}, "source": [ - "Let's see the result of a large number of $n$s to see the changes with an increasing $n$.\n", + "We can see that the distribution of $\\bar X$ is clustered around $\\mathbb E X$ as expected.\n", "\n", - "You can imagine the result when extrapolating this trend for $(n \\to \\infty)$." + "We can increase values for `n` and `m` to see how the distribution changes by slightly changing the code to see the changes with an increasing $n$" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": null, "id": "597a28c8-046e-44d4-b4ce-4bf1d580601c", "metadata": {}, "outputs": [], @@ -427,7 +390,7 @@ " sample_means = [draw_means(X_distribution, n) for i in range(m)]\n", " if log_scale:\n", " plt.xscale('symlog')\n", - " ax.hist(sample_means, bins=60, alpha=0.4, density=True, label=fr'$n = {n}, m = {m}$')\n", + " ax.hist(sample_means, bins=60, alpha=0.4, density=True, label=fr'$n = {n}$')\n", " \n", " mu = X_distribution.mean()\n", " if not np.isnan(mu):\n", @@ -443,25 +406,24 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": null, "id": "7dbed08d-3560-4f6d-8bb9-7c3ee75bab43", "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "generate_multiple_hist(st.norm(loc=5, scale=2), ns=[20_000, 50_000, 100_000], m=10_000)" ] }, + { + "cell_type": "markdown", + "id": "f8c6e4b4-344b-497e-bc71-ecac322be3c8", + "metadata": {}, + "source": [ + "We see that the histogram gradually converge to $\\mu$.\n", + "\n", + "You can imagine the result when extrapolating this trend for $(n \\to \\infty)$." + ] + }, { "cell_type": "markdown", "id": "22987bd7", @@ -473,33 +435,7 @@ "\n", "As indicated by {eq}`lln_as`, LLN can break when $\\mathbb E |X|$ is not finite or is not well defined.\n", "\n", - "We can demonstrate this using a simple simulation using a [Cauchy distribution](https://en.wikipedia.org/wiki/Cauchy_distribution) for which it does not have a well-defined $\\mu$.\n", - "\n", - "TODO\n", - "\n", - "* Illustrate by simulation that the LLN can fail when the population mean is not finite\n", - "* Illustrate by simulation that the IID assumption is important" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "838fbcc4-691c-45ed-bd20-a853f1953c7e", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "generate_multiple_hist(st.cauchy(), ns=[20_000, 50_000, 100_000], m=10_000, log_scale=True)" + "We can demonstrate this using a simple simulation using a [Cauchy distribution](https://en.wikipedia.org/wiki/Cauchy_distribution) for which it does not have a well-defined $\\mu$." ] }, { @@ -507,20 +443,18 @@ "id": "dddea715-be50-4d63-82e7-b51115b2c9cf", "metadata": {}, "source": [ - "We lost the convergence we have before for normal distribution\n", - "\n", - "A scattered plot can better show us why this is the case" + "We lost the convergence we have seen before with normal distribution " ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 15, "id": "dda56a48-d06c-4ed4-9c7e-180d843d1d63", "metadata": {}, "outputs": [ { "data": { - "image/png": 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"text/plain": [ "
" ] @@ -532,36 +466,38 @@ "source": [ "fig, axes = plt.subplots(1, 2, figsize=(15, 6))\n", "\n", - "def scattered_mean(distribution, burn_in, n, jump, ax, title, ylog=False):\n", + "def scattered_mean(distribution, burn_in, n, jump, ax, title, color, ylog=False):\n", " \n", " #Set a jump to reduce simulation complexity\n", " sample_means = [np.mean(distribution.rvs(size=i)) \n", " for i in range(burn_in, n+1, jump)]\n", " \n", - " ax.scatter(range(burn_in, n+1, jump), sample_means, s=10)\n", + " ax.scatter(range(burn_in, n+1, jump), sample_means, s=10, c=color)\n", " if ylog:\n", " ax.set_yscale(\"symlog\")\n", " ax.set_title(title, size=10)\n", - " ax.set_xlabel(\"Sample Size\")\n", - " ax.set_ylabel(\"Sample Mean\")\n", + " ax.set_xlabel(r\"$n$\", size=12)\n", + " ax.set_ylabel(r\"$\\bar x$\", size=12)\n", " yabs_max = max(ax.get_ylim(), key=abs)\n", " ax.set_ylim(ymin=-yabs_max, ymax=yabs_max)\n", " return ax\n", "\n", "scattered_mean(distribution=st.cauchy(), \n", - " burn_in=10_000, \n", + " burn_in=1000, \n", " n=1_000_000, \n", " ax=axes[0],\n", - " jump=1000,\n", + " jump=2000,\n", " title=\"Cauchy Distribution\",\n", + " color='#1f77b4',\n", " ylog=True)\n", "\n", "scattered_mean(distribution=st.norm(), \n", - " burn_in=10_000, \n", + " burn_in=1000, \n", " n=1_000_000,\n", " ax=axes[1],\n", - " jump=1000,\n", - " title=\"Normal Distribution\")\n", + " jump=2000,\n", + " title=\"Normal Distribution\",\n", + " color='#ff7f0e')\n", "\n", "fig.suptitle('Sample Mean with Different Sample Size')\n", "plt.show()" @@ -574,58 +510,77 @@ "source": [ "We can see that unlike normal distribution, Cauchy distribution does not have a convergence that LLN implies.\n", "\n", - "It is also not hard to conjecture that LLN can be broken when the IID assumption is violated.\n", - "\n", - "We can go through an example that involves" + "It is also not hard to conjecture that LLN can be broken when the IID assumption is violated." ] }, { - "cell_type": "code", - "execution_count": 12, - "id": "5a0232ff-da52-4374-8506-609593db6bd7", + "cell_type": "markdown", + "id": "d9f61c65-b2d8-4989-95dd-0837b635e9ff", "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], "source": [ - "n = 1_000_000\n", + "Let's go through a very simple example where LLN fails with IID violated:\n", "\n", - "def iid_comparison(n, p):\n", - " samples = np.zeros(n+1)\n", - " X_draws = st.bernoulli.rvs(p, size=n)\n", - " _, ax = plt.subplots(figsize=(10, 6))\n", + "Assume\n", "\n", - " for i in range(n):\n", - " # Dependency\n", - " if samples[i] > 5:\n", - " samples[i+1] = st.norm.rvs(loc=5, scale=2, size=1)\n", - " else:\n", - " samples[i+1] = st.norm.rvs(loc=10, scale=2, size=1)\n", + "$$\n", + "X_1 \\sim \\mathcal{N}(0,1)\n", + "$$\n", "\n", - " # Plot the stock prices without iid assumption\n", - " ax.hist(samples, label=\"non-iid\", bins=60, alpha=0.5, density=True)\n", - " distribution = st.norm(loc=5, scale=2)\n", - " ax.hist(distribution.rvs(size=n), bins=60, label=\"iid\", alpha=0.5, density=True)\n", + "In addition, assume\n", "\n", - " # Add labels and legend\n", - " ax.set_xlabel(r'$\\bar x$')\n", - " ax.set_ylabel('Density')\n", - " ax.axvline(x=distribution.mean(), ls=\"--\", lw=3, label=fr\"$\\mu = {distribution.mean()}$\")\n", - " ax.legend()\n", + "$$\n", + "X_t = X_{t-1} \\quad \\text{for} \\quad t = 2, ..., n\n", + "$$\n", "\n", - " # Show the plot\n", - " plt.show()\n", - " \n", - "iid_comparison(n, 0.9)" + "We can then see that \n", + "\n", + "$$\n", + "\\bar X_n := \\frac{1}{T} \\sum_{t=1}^n X_i = X_1 \\sim \\mathcal{N}(0,1)\n", + "$$\n", + "\n", + "Therefore, the distribution of mean of X follows $\\mathcal{N}(0,1)$.\n", + "\n", + "However,\n", + "\n", + "$$\n", + "\\mathbb E X_t = \\mathbb E X_1 = 0\n", + "$$\n", + "\n", + "which violates {eq}`exp`, and thus breaks LLN.\n", + "\n", + "```{note}\n", + "Although in this case, the violation of IID breaks LLN, it is not always the case for correlated data (TODO: Link to MC Lecture)\n", + "```" + ] + }, + { + "cell_type": "markdown", + "id": "16435333-a22f-4cd5-8d90-699e813585f9", + "metadata": { + "tags": [] + }, + "source": [ + "## LLN and CLT\n", + "\n", + "## Overview\n", + "\n", + "This lecture illustrates two of the most important theorems of probability and statistics: The\n", + "law of large numbers (LLN) and the central limit theorem (CLT).\n", + "\n", + "These beautiful theorems lie behind many of the most fundamental results in econometrics and quantitative economic modeling.\n", + "\n", + "The lecture is based around simulations that show the LLN and CLT in action.\n", + "\n", + "We also demonstrate how the LLN and CLT break down when the assumptions they are based on do not hold.\n", + "\n", + "In addition, we examine several useful extensions of the classical theorems, such as\n", + "\n", + "* The delta method, for smooth functions of random variables, and\n", + "* the multivariate case.\n", + "\n", + "Some of these extensions are presented as exercises.\n", + "\n", + "We'll need the following imports:" ] }, { @@ -706,21 +661,10 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": null, "id": "c6444237", "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "# Set parameters\n", "n = 250 # Choice of n\n", @@ -791,18 +735,10 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": null, "id": "1b300696", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "1\n" - ] - } - ], + "outputs": [], "source": [ "U = np.random.rand()\n", "X = 1 if U < p else 0\n", diff --git a/in-work/lln_clt.md b/in-work/lln_clt.md index 813d3e953..2d1c083ad 100644 --- a/in-work/lln_clt.md +++ b/in-work/lln_clt.md @@ -1,14 +1,15 @@ --- -jupytext: - text_representation: - extension: .md - format_name: myst - format_version: 0.13 - jupytext_version: 1.14.1 -kernelspec: - display_name: Python 3 (ipykernel) - language: python - name: python3 +jupyter: + jupytext: + text_representation: + extension: .md + format_name: markdown + format_version: '1.3' + jupytext_version: 1.14.4 + kernelspec: + display_name: Python 3 (ipykernel) + language: python + name: python3 --- ## LLN and CLT @@ -33,13 +34,14 @@ Some of these extensions are presented as exercises. We'll need the following imports: -```{code-cell} ipython3 +```python import matplotlib.pyplot as plt import random import numpy as np import scipy.stats as st ``` + ## Relationships @@ -76,8 +78,9 @@ $$ $$ We can generate a draw of $X$ with `scipy.stats` (imported as `st`) as follows: + -```{code-cell} ipython3 +```python p = 0.8 X = st.bernoulli.rvs(p) print(X) @@ -87,7 +90,7 @@ In this setting, the LLN tells us if we flip the coin many times, the fraction o Let's check this: -```{code-cell} ipython3 +```python n = 1_000_000 X_draws = st.bernoulli.rvs(p, size=n) print(X_draws.mean()) # count the number of 1's and divide by n @@ -95,7 +98,7 @@ print(X_draws.mean()) # count the number of 1's and divide by n If we change $p$ the claim still holds: -```{code-cell} ipython3 +```python p = 0.3 X_draws = st.bernoulli.rvs(p, size=n) print(X_draws.mean()) @@ -115,15 +118,16 @@ which, in this case, is the fraction of draws that equal one (the number of head Thus, the LLN tells us that -$$ +```{math} +:label: exp + \bar X_n \to \mathbb E X = p \qquad (n \to \infty) -$$ +``` This is exactly what we illustrated in the code above. -+++ - + (lln_ksl)= ### Statement of the LLN @@ -137,6 +141,7 @@ This random variables can be continuous or discrete. For simplicity we will assume they are continuous and we let $f$ denote their density function, so that, for any $i$ in $\{1, \ldots, n\}$ + $$ \mathbb P\{a \leq X_i \leq b\} = \int_a^b f(x) dx $$ @@ -176,9 +181,9 @@ Let's also imagine that we can generate infinite sequences so that the statement In this setting, {eq}`lln_as` should be interpreted as meaning that the probability of the computer producing a sequence where $\bar X_n \to \mu$ fails to occur is zero. + -+++ - + ### Illustration ```{index} single: Law of Large Numbers; Illustration @@ -186,7 +191,7 @@ is zero. Let's now illustrate the LLN using simulation. -When we illustrate it, we will use a key idea: the sample mean $\bar X_n$ is itself a random variable. +When we illustrate it, we will use a key idea: the sample mean $\bar X$ is itself a random variable. In a sense this is obvious but it can be easy to forget. @@ -210,21 +215,201 @@ Moreover, if we repeat the exercise with a larger value of $n$, we should see th This is, in essence, what the LLN is telling us. +Let's run some simulations to visualize LLN + +Let's + + +```python +def generate_histogram(X_distribution, n, m): + fig, ax = plt.subplots(figsize=(10, 6)) + + def draw_means(X_distribution, n): + + # Step 3: Generate n draws: X_1, ..., X_n + X_samples = X_distribution.rvs(size=n) + + # Step 4: Calculate sample mean + return np.mean(X_samples) + + # Step 5: Loop m times + sample_means = [draw_means(X_distribution, n) for i in range(m)] + print(f'The mean of sample mean is {round(np.mean(sample_means),2)}') + + # Generate a histogram + ax.hist(sample_means, bins=30, alpha=0.5, density=True) + mu = X_distribution.mean() + if not np.isnan(mu): + ax.axvline(x=mu, ls="--", lw=3, label=fr"$\mu = {mu}$") + + ax.set_xlim(min(sample_means), max(sample_means)) + ax.set_xlabel(r'$\bar x$') + ax.set_ylabel('Density') + ax.legend() + plt.show() +``` -```{code-cell} ipython3 -# TODO: write the code and put the plot here +```python +#Step 1: Pick some distribution to draw each $X_i$ from +#Step 2: Set $n$ to some large number +generate_histogram(st.norm(loc=5, scale=2), n=50_000, m=1000) ``` +We can see that the distribution of $\bar X$ is clustered around $\mathbb E X$ as expected. + +We can increase values for `n` and `m` to see how the distribution changes by slightly changing the code to see the changes with an increasing $n$ + +```python +def generate_multiple_hist(X_distribution, ns, m, log_scale=False): + _, ax = plt.subplots(figsize=(10, 6)) + + def draw_means(X_distribution, n): + X_samples = X_distribution.rvs(size=n) + return np.mean(X_samples) + + for n in ns: + sample_means = [draw_means(X_distribution, n) for i in range(m)] + if log_scale: + plt.xscale('symlog') + ax.hist(sample_means, bins=60, alpha=0.4, density=True, label=fr'$n = {n}$') + + mu = X_distribution.mean() + if not np.isnan(mu): + ax.axvline(x=mu, ls="--", lw=3, label=fr"$\mu = {mu}$") + + ax.set_xlim(min(sample_means), max(sample_means)) + ax.set_xlabel(r'$\bar x$') + ax.set_ylabel('Density') + ax.set(title=fr'$n = {n}, m = {m}$') + ax.legend() + plt.show() +``` + +```python +generate_multiple_hist(st.norm(loc=5, scale=2), ns=[20_000, 50_000, 100_000], m=10_000) +``` + +We see that the histogram gradually converge to $\mu$. + +You can imagine the result when extrapolating this trend for $(n \to \infty)$. + + ## Breaking the LLN We have to pay attention to the assumptions in the statement of the LLN when we apply it. -TODO +As indicated by {eq}`lln_as`, LLN can break when $\mathbb E |X|$ is not finite or is not well defined. + +We can demonstrate this using a simple simulation using a [Cauchy distribution](https://en.wikipedia.org/wiki/Cauchy_distribution) for which it does not have a well-defined $\mu$. + + +We lost the convergence we have seen before with normal distribution + +```python +fig, axes = plt.subplots(1, 2, figsize=(15, 6)) + +def scattered_mean(distribution, burn_in, n, jump, ax, title, color, ylog=False): + + #Set a jump to reduce simulation complexity + sample_means = [np.mean(distribution.rvs(size=i)) + for i in range(burn_in, n+1, jump)] + + ax.scatter(range(burn_in, n+1, jump), sample_means, s=10, c=color) + if ylog: + ax.set_yscale("symlog") + ax.set_title(title, size=10) + ax.set_xlabel(r"$n$", size=12) + ax.set_ylabel(r"$\bar x$", size=12) + yabs_max = max(ax.get_ylim(), key=abs) + ax.set_ylim(ymin=-yabs_max, ymax=yabs_max) + return ax + +scattered_mean(distribution=st.cauchy(), + burn_in=1000, + n=1_000_000, + ax=axes[0], + jump=2000, + title="Cauchy Distribution", + color='#1f77b4', + ylog=True) + +scattered_mean(distribution=st.norm(), + burn_in=1000, + n=1_000_000, + ax=axes[1], + jump=2000, + title="Normal Distribution", + color='#ff7f0e') + +fig.suptitle('Sample Mean with Different Sample Size') +plt.show() +``` + +We can see that unlike normal distribution, Cauchy distribution does not have a convergence that LLN implies. + +It is also not hard to conjecture that LLN can be broken when the IID assumption is violated. + + +Let's go through a very simple example where LLN fails with IID violated: + +Assume + +$$ +X_1 \sim \mathcal{N}(0,1) +$$ + +In addition, assume + +$$ +X_t = X_{t-1} \quad \text{for} \quad t = 2, ..., n +$$ + +We can then see that + +$$ +\bar X_n := \frac{1}{T} \sum_{t=1}^n X_i = X_1 \sim \mathcal{N}(0,1) +$$ -* Illustrate by simulation that the LLN can fail when the population mean is not finite -* Illustrate by simulation that the IID assumption is important +Therefore, the distribution of mean of X follows $\mathcal{N}(0,1)$. + +However, + +$$ +\mathbb E X_t = \mathbb E X_1 = 0 +$$ + +which violates {eq}`exp`, and thus breaks LLN. + +```{note} +Although in this case, the violation of IID breaks LLN, it is not always the case for correlated data (TODO: Link to MC Lecture) +``` + + +## LLN and CLT + +## Overview + +This lecture illustrates two of the most important theorems of probability and statistics: The +law of large numbers (LLN) and the central limit theorem (CLT). + +These beautiful theorems lie behind many of the most fundamental results in econometrics and quantitative economic modeling. + +The lecture is based around simulations that show the LLN and CLT in action. + +We also demonstrate how the LLN and CLT break down when the assumptions they are based on do not hold. + +In addition, we examine several useful extensions of the classical theorems, such as + +* The delta method, for smooth functions of random variables, and +* the multivariate case. + +Some of these extensions are presented as exercises. + +We'll need the following imports: + + +In this case, since the samples are neither drawn independently nor identically distributed, and the converging trend towards $\mu$ is not found. -+++ ## CLT @@ -264,8 +449,6 @@ The striking implication of the CLT is that for **any** distribution with finite second moment, the simple operation of adding independent copies **always** leads to a Gaussian curve. -+++ - ### Simulation 1 @@ -285,12 +468,12 @@ $F(x) = 1 - e^{- \lambda x}$. (sim_one)= -```{code-cell} ipython3 +```python # Set parameters n = 250 # Choice of n k = 1_000_000 # Number of draws of Y_n distribution = st.expon(2) # Exponential distribution, λ = 1/2 -μ, s = distribution.mean(), distribution.std() +μ, σ = distribution.mean(), distribution.std() # Draw underlying RVs. Each row contains a draw of X_1,..,X_n data = distribution.rvs((k, n)) @@ -301,11 +484,11 @@ Y = np.sqrt(n) * (sample_means - μ) # Plot fig, ax = plt.subplots(figsize=(10, 6)) -xmin, xmax = -3 * s, 3 * s +xmin, xmax = -3 * σ, 3 * σ ax.set_xlim(xmin, xmax) ax.hist(Y, bins=60, alpha=0.4, density=True) xgrid = np.linspace(xmin, xmax, 200) -ax.plot(xgrid, st.norm.pdf(xgrid, scale=s), 'k-', lw=2, label='$N(0, \sigma^2)$') +ax.plot(xgrid, st.norm.pdf(xgrid, scale=σ), 'k-', lw=2, label='$N(0, \sigma^2)$') ax.legend() plt.show() @@ -316,24 +499,18 @@ plt.show() The fit to the normal density is already tight and can be further improved by increasing `n`. - -+++ - ## Exercises -+++ ## Ex 1 -+++ -As the reader to rerun the last simulation and experiment with other specifications of $F$ that have finite second moment, making sure that they +As the reader to rerun the last simulation and experiment with other specifications of $F$ that have finite second moment, making sure that they -+++ Although NumPy doesn't give us a `bernoulli` function, we can generate a draw of $X$ using NumPy via -```{code-cell} ipython3 +```python U = np.random.rand() X = 1 if U < p else 0 print(X) @@ -341,11 +518,9 @@ print(X) Explain why this provides a random variable $X$ with the right distribution. -+++ Solution: -+++ We can write $X$ as $X = \mathbf 1\{U < p\}$ where $\mathbf 1$ is the [indicator function](https://en.wikipedia.org/wiki/Indicator_function) (i.e., 1 if the statement is true and zero otherwise). @@ -357,7 +532,6 @@ $$ This means that $X = \mathbf 1\{U < p\}$ has the right distribution. -+++ ```{solution-end} ``` From 0ee00fc458afa803f8e2ecb82d420cbfa5528e71 Mon Sep 17 00:00:00 2001 From: Humphrey Yang Date: Tue, 31 Jan 2023 16:40:45 +1100 Subject: [PATCH 04/12] update lln_clt --- in-work/lln_clt.ipynb | 177 ++++++++++++++++++---------- in-work/lln_clt.md | 262 +++++++++++++++++++++--------------------- 2 files changed, 249 insertions(+), 190 deletions(-) diff --git a/in-work/lln_clt.ipynb b/in-work/lln_clt.ipynb index 70598c5c6..914efe702 100644 --- a/in-work/lln_clt.ipynb +++ b/in-work/lln_clt.ipynb @@ -124,7 +124,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "0.800251\n" + "0.799764\n" ] } ], @@ -152,7 +152,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "0.299723\n" + "0.299568\n" ] } ], @@ -292,14 +292,12 @@ "\n", "This is, in essence, what the LLN is telling us.\n", "\n", - "Let's run some simulations to visualize LLN\n", - "\n", - "Let's" + "Let's run some simulations to visualize LLN" ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 5, "id": "9299240a", "metadata": {}, "outputs": [], @@ -334,7 +332,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 6, "id": "0b0da74f-1f3d-4b75-bb4a-86c85c4539bb", "metadata": {}, "outputs": [ @@ -347,7 +345,7 @@ }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -374,7 +372,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "id": "597a28c8-046e-44d4-b4ce-4bf1d580601c", "metadata": {}, "outputs": [], @@ -395,7 +393,7 @@ " mu = X_distribution.mean()\n", " if not np.isnan(mu):\n", " ax.axvline(x=mu, ls=\"--\", lw=3, label=fr\"$\\mu = {mu}$\")\n", - " \n", + " \n", " ax.set_xlim(min(sample_means), max(sample_means)) \n", " ax.set_xlabel(r'$\\bar x$')\n", " ax.set_ylabel('Density')\n", @@ -406,10 +404,21 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "id": "7dbed08d-3560-4f6d-8bb9-7c3ee75bab43", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "generate_multiple_hist(st.norm(loc=5, scale=2), ns=[20_000, 50_000, 100_000], m=10_000)" ] @@ -421,7 +430,7 @@ "source": [ "We see that the histogram gradually converge to $\\mu$.\n", "\n", - "You can imagine the result when extrapolating this trend for $(n \\to \\infty)$." + "You can imagine the result when extrapolating this trend for $n \\to \\infty$." ] }, { @@ -448,13 +457,13 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 9, "id": "dda56a48-d06c-4ed4-9c7e-180d843d1d63", "metadata": {}, "outputs": [ { "data": { - "image/png": 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" ] @@ -473,6 +482,8 @@ " for i in range(burn_in, n+1, jump)]\n", " \n", " ax.scatter(range(burn_in, n+1, jump), sample_means, s=10, c=color)\n", + " \n", + " #Change the y-axis to log scale if necessory\n", " if ylog:\n", " ax.set_yscale(\"symlog\")\n", " ax.set_title(title, size=10)\n", @@ -535,7 +546,7 @@ "We can then see that \n", "\n", "$$\n", - "\\bar X_n := \\frac{1}{T} \\sum_{t=1}^n X_i = X_1 \\sim \\mathcal{N}(0,1)\n", + "\\bar X_n := \\frac{1}{n} \\sum_{t=1}^n X_i = X_1 \\sim \\mathcal{N}(0,1)\n", "$$\n", "\n", "Therefore, the distribution of mean of X follows $\\mathcal{N}(0,1)$.\n", @@ -553,44 +564,6 @@ "```" ] }, - { - "cell_type": "markdown", - "id": "16435333-a22f-4cd5-8d90-699e813585f9", - "metadata": { - "tags": [] - }, - "source": [ - "## LLN and CLT\n", - "\n", - "## Overview\n", - "\n", - "This lecture illustrates two of the most important theorems of probability and statistics: The\n", - "law of large numbers (LLN) and the central limit theorem (CLT).\n", - "\n", - "These beautiful theorems lie behind many of the most fundamental results in econometrics and quantitative economic modeling.\n", - "\n", - "The lecture is based around simulations that show the LLN and CLT in action.\n", - "\n", - "We also demonstrate how the LLN and CLT break down when the assumptions they are based on do not hold.\n", - "\n", - "In addition, we examine several useful extensions of the classical theorems, such as\n", - "\n", - "* The delta method, for smooth functions of random variables, and\n", - "* the multivariate case.\n", - "\n", - "Some of these extensions are presented as exercises.\n", - "\n", - "We'll need the following imports:" - ] - }, - { - "cell_type": "markdown", - "id": "c435af34-8366-410b-b4d8-793665d8dd0b", - "metadata": {}, - "source": [ - "In this case, since the samples are neither drawn independently nor identically distributed, and the converging trend towards $\\mu$ is not found." - ] - }, { "cell_type": "markdown", "id": "59934170", @@ -638,7 +611,9 @@ { "cell_type": "markdown", "id": "928cdff7", - "metadata": {}, + "metadata": { + "tags": [] + }, "source": [ "### Simulation 1\n", "\n", @@ -661,10 +636,21 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "id": "c6444237", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# Set parameters\n", "n = 250 # Choice of n\n", @@ -711,7 +697,7 @@ }, { "cell_type": "markdown", - "id": "b49befe8", + "id": "89258210-db73-4470-85a7-033b21a072b1", "metadata": {}, "source": [ "## Ex 1" @@ -719,10 +705,69 @@ }, { "cell_type": "markdown", - "id": "57710f7b", + "id": "40206358-6c49-4a4c-9c81-a6ae70d9c8fe", + "metadata": {}, + "source": [ + "Repeat the simulation in (TODO: Add a reference) with [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution). " + ] + }, + { + "cell_type": "markdown", + "id": "f65d6d4a-4aa4-4ce1-b047-21b8eb682cd9", + "metadata": {}, + "source": [ + "Solution:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "95967ca5-c970-4236-b8e4-6296989dc81f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Set parameters\n", + "n = 250 # Choice of n\n", + "k = 1_000_000 # Number of draws of Y_n\n", + "distribution = st.beta(2,2) # Exponential distribution, λ = 1/2\n", + "μ, σ = distribution.mean(), distribution.std()\n", + "\n", + "# Draw underlying RVs. Each row contains a draw of X_1,..,X_n\n", + "data = distribution.rvs((k, n))\n", + "# Compute mean of each row, producing k draws of \\bar X_n\n", + "sample_means = data.mean(axis=1)\n", + "# Generate observations of Y_n\n", + "Y = np.sqrt(n) * (sample_means - μ)\n", + "\n", + "# Plot\n", + "fig, ax = plt.subplots(figsize=(10, 6))\n", + "xmin, xmax = -3 * σ, 3 * σ\n", + "ax.set_xlim(xmin, xmax)\n", + "ax.hist(Y, bins=60, alpha=0.4, density=True)\n", + "xgrid = np.linspace(xmin, xmax, 200)\n", + "ax.plot(xgrid, st.norm.pdf(xgrid, scale=σ), 'k-', lw=2, label='$N(0, \\sigma^2)$')\n", + "ax.legend()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "b49befe8", "metadata": {}, "source": [ - "As the reader to rerun the last simulation and experiment with other specifications of $F$ that have finite second moment, making sure that they" + "## Ex 2" ] }, { @@ -735,10 +780,18 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "id": "1b300696", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0\n" + ] + } + ], "source": [ "U = np.random.rand()\n", "X = 1 if U < p else 0\n", diff --git a/in-work/lln_clt.md b/in-work/lln_clt.md index 2d1c083ad..f9c4c5ac5 100644 --- a/in-work/lln_clt.md +++ b/in-work/lln_clt.md @@ -1,15 +1,15 @@ --- jupyter: - jupytext: - text_representation: - extension: .md - format_name: markdown - format_version: '1.3' - jupytext_version: 1.14.4 - kernelspec: - display_name: Python 3 (ipykernel) - language: python - name: python3 + jupytext: + text_representation: + extension: .md + format_name: markdown + format_version: '1.3' + jupytext_version: 1.14.4 + kernelspec: + display_name: Python 3 (ipykernel) + language: python + name: python3 --- ## LLN and CLT @@ -93,7 +93,7 @@ Let's check this: ```python n = 1_000_000 X_draws = st.bernoulli.rvs(p, size=n) -print(X_draws.mean()) # count the number of 1's and divide by n +print(X_draws.mean()) # count the number of 1's and divide by n ``` If we change $p$ the claim still holds: @@ -137,13 +137,13 @@ The traditional version of the law of large numbers concerns independent and ide Let $X_1, \ldots, X_n$ be independent and identically distributed random variables. -This random variables can be continuous or discrete. +These random variables can be continuous or discrete. -For simplicity we will assume they are continuous and we let $f$ denote their density function, so that, for any $i$ in $\{1, \ldots, n\}$ +For simplicity we will assume they are continuous, and we let $f$ denote their density function, so that, for any $i$ in $\{1, \ldots, n\}$ $$ - \mathbb P\{a \leq X_i \leq b\} = \int_a^b f(x) dx + \mathbb P\{a \leq X_i \leq b\} = \int_a^b f(x) dx $$ (For the discrete case, we need to replace densities with probability mass functions and integrals with sums.) @@ -151,7 +151,7 @@ $$ Let $\mu$ denote the common mean of this sample: $$ - \mu := \mathbb E X = \int_{-\infty}^{\infty} x f(dx) + \mu := \mathbb E X = \int_{-\infty}^{\infty} x f(dx) $$ In addition, let @@ -216,37 +216,35 @@ Moreover, if we repeat the exercise with a larger value of $n$, we should see th This is, in essence, what the LLN is telling us. Let's run some simulations to visualize LLN - -Let's ```python def generate_histogram(X_distribution, n, m): - fig, ax = plt.subplots(figsize=(10, 6)) - - def draw_means(X_distribution, n): - - # Step 3: Generate n draws: X_1, ..., X_n - X_samples = X_distribution.rvs(size=n) - - # Step 4: Calculate sample mean - return np.mean(X_samples) - - # Step 5: Loop m times - sample_means = [draw_means(X_distribution, n) for i in range(m)] - print(f'The mean of sample mean is {round(np.mean(sample_means),2)}') - - # Generate a histogram - ax.hist(sample_means, bins=30, alpha=0.5, density=True) - mu = X_distribution.mean() - if not np.isnan(mu): - ax.axvline(x=mu, ls="--", lw=3, label=fr"$\mu = {mu}$") - - ax.set_xlim(min(sample_means), max(sample_means)) - ax.set_xlabel(r'$\bar x$') - ax.set_ylabel('Density') - ax.legend() - plt.show() + fig, ax = plt.subplots(figsize=(10, 6)) + + def draw_means(X_distribution, n): + + # Step 3: Generate n draws: X_1, ..., X_n + X_samples = X_distribution.rvs(size=n) + + # Step 4: Calculate the sample mean + return np.mean(X_samples) + + # Step 5: Loop m times + sample_means = [draw_means(X_distribution, n) for i in range(m)] + print(f'The mean of sample mean is {round(np.mean(sample_means),2)}') + + # Generate a histogram + ax.hist(sample_means, bins=30, alpha=0.5, density=True) + mu = X_distribution.mean() + if not np.isnan(mu): + ax.axvline(x=mu, ls="--", lw=3, label=fr"$\mu = {mu}$") + + ax.set_xlim(min(sample_means), max(sample_means)) + ax.set_xlabel(r'$\bar x$') + ax.set_ylabel('Density') + ax.legend() + plt.show() ``` ```python @@ -261,37 +259,37 @@ We can increase values for `n` and `m` to see how the distribution changes by sl ```python def generate_multiple_hist(X_distribution, ns, m, log_scale=False): - _, ax = plt.subplots(figsize=(10, 6)) - - def draw_means(X_distribution, n): - X_samples = X_distribution.rvs(size=n) - return np.mean(X_samples) - - for n in ns: - sample_means = [draw_means(X_distribution, n) for i in range(m)] - if log_scale: - plt.xscale('symlog') - ax.hist(sample_means, bins=60, alpha=0.4, density=True, label=fr'$n = {n}$') - - mu = X_distribution.mean() - if not np.isnan(mu): - ax.axvline(x=mu, ls="--", lw=3, label=fr"$\mu = {mu}$") - - ax.set_xlim(min(sample_means), max(sample_means)) - ax.set_xlabel(r'$\bar x$') - ax.set_ylabel('Density') - ax.set(title=fr'$n = {n}, m = {m}$') - ax.legend() - plt.show() + _, ax = plt.subplots(figsize=(10, 6)) + + def draw_means(X_distribution, n): + X_samples = X_distribution.rvs(size=n) + return np.mean(X_samples) + + for n in ns: + sample_means = [draw_means(X_distribution, n) for i in range(m)] + if log_scale: + plt.xscale('symlog') + ax.hist(sample_means, bins=60, alpha=0.4, density=True, label=fr'$n = {n}$') + + mu = X_distribution.mean() + if not np.isnan(mu): + ax.axvline(x=mu, ls="--", lw=3, label=fr"$\mu = {mu}$") + + ax.set_xlim(min(sample_means), max(sample_means)) + ax.set_xlabel(r'$\bar x$') + ax.set_ylabel('Density') + ax.set(title=fr'$n = {n}, m = {m}$') + ax.legend() + plt.show() ``` ```python generate_multiple_hist(st.norm(loc=5, scale=2), ns=[20_000, 50_000, 100_000], m=10_000) ``` -We see that the histogram gradually converge to $\mu$. +We see that from the histogram that it gradually converges to $\mu$. -You can imagine the result when extrapolating this trend for $(n \to \infty)$. +You can imagine the result when extrapolating this trend for $n \to \infty$. ## Breaking the LLN @@ -309,48 +307,50 @@ We lost the convergence we have seen before with normal distribution fig, axes = plt.subplots(1, 2, figsize=(15, 6)) def scattered_mean(distribution, burn_in, n, jump, ax, title, color, ylog=False): - - #Set a jump to reduce simulation complexity - sample_means = [np.mean(distribution.rvs(size=i)) - for i in range(burn_in, n+1, jump)] - - ax.scatter(range(burn_in, n+1, jump), sample_means, s=10, c=color) - if ylog: - ax.set_yscale("symlog") - ax.set_title(title, size=10) - ax.set_xlabel(r"$n$", size=12) - ax.set_ylabel(r"$\bar x$", size=12) - yabs_max = max(ax.get_ylim(), key=abs) - ax.set_ylim(ymin=-yabs_max, ymax=yabs_max) - return ax + + #Set a jump to reduce simulation complexity + sample_means = [np.mean(distribution.rvs(size=i)) + for i in range(burn_in, n+1, jump)] + + ax.scatter(range(burn_in, n+1, jump), sample_means, s=10, c=color) + + #Change the y-axis to log scale if necessary + if ylog: + ax.set_yscale("symlog") + ax.set_title(title, size=10) + ax.set_xlabel(r"$n$", size=12) + ax.set_ylabel(r"$\bar x$", size=12) + yabs_max = max(ax.get_ylim(), key=abs) + ax.set_ylim(ymin=-yabs_max, ymax=yabs_max) + return ax scattered_mean(distribution=st.cauchy(), - burn_in=1000, - n=1_000_000, - ax=axes[0], - jump=2000, - title="Cauchy Distribution", - color='#1f77b4', - ylog=True) + burn_in=1000, + n=1_000_000, + ax=axes[0], + jump=2000, + title="Cauchy Distribution", + color='#1f77b4', + ylog=True) scattered_mean(distribution=st.norm(), - burn_in=1000, - n=1_000_000, - ax=axes[1], - jump=2000, - title="Normal Distribution", - color='#ff7f0e') + burn_in=1000, + n=1_000_000, + ax=axes[1], + jump=2000, + title="Normal Distribution", + color='#ff7f0e') fig.suptitle('Sample Mean with Different Sample Size') plt.show() ``` -We can see that unlike normal distribution, Cauchy distribution does not have a convergence that LLN implies. +We can see that, unlike normal distribution, the Cauchy distribution does not have the convergence that LLN implies. It is also not hard to conjecture that LLN can be broken when the IID assumption is violated. -Let's go through a very simple example where LLN fails with IID violated: +Let's go through a very simple example where LLN fails with the IID violated: Assume @@ -367,10 +367,10 @@ $$ We can then see that $$ -\bar X_n := \frac{1}{T} \sum_{t=1}^n X_i = X_1 \sim \mathcal{N}(0,1) +\bar X_n := \frac{1}{n} \sum_{t=1}^n X_i = X_1 \sim \mathcal{N}(0,1) $$ -Therefore, the distribution of mean of X follows $\mathcal{N}(0,1)$. +Therefore, the distribution of the mean of X follows $\mathcal{N}(0,1)$. However, @@ -384,32 +384,6 @@ which violates {eq}`exp`, and thus breaks LLN. Although in this case, the violation of IID breaks LLN, it is not always the case for correlated data (TODO: Link to MC Lecture) ``` - -## LLN and CLT - -## Overview - -This lecture illustrates two of the most important theorems of probability and statistics: The -law of large numbers (LLN) and the central limit theorem (CLT). - -These beautiful theorems lie behind many of the most fundamental results in econometrics and quantitative economic modeling. - -The lecture is based around simulations that show the LLN and CLT in action. - -We also demonstrate how the LLN and CLT break down when the assumptions they are based on do not hold. - -In addition, we examine several useful extensions of the classical theorems, such as - -* The delta method, for smooth functions of random variables, and -* the multivariate case. - -Some of these extensions are presented as exercises. - -We'll need the following imports: - - -In this case, since the samples are neither drawn independently nor identically distributed, and the converging trend towards $\mu$ is not found. - ## CLT @@ -449,7 +423,7 @@ The striking implication of the CLT is that for **any** distribution with finite second moment, the simple operation of adding independent copies **always** leads to a Gaussian curve. - + ### Simulation 1 Since the CLT seems almost magical, running simulations that verify its implications is one good way to build intuition. @@ -467,12 +441,13 @@ $F(x) = 1 - e^{- \lambda x}$. (Please experiment with other choices of $F$, but remember that, to conform with the conditions of the CLT, the distribution must have a finite second moment.) (sim_one)= + ```python # Set parameters -n = 250 # Choice of n -k = 1_000_000 # Number of draws of Y_n -distribution = st.expon(2) # Exponential distribution, λ = 1/2 +n = 250 # Choice of n +k = 1_000_000 # Number of draws of Y_n +distribution = st.expon(2) # Exponential distribution, λ = 1/2 μ, σ = distribution.mean(), distribution.std() # Draw underlying RVs. Each row contains a draw of X_1,..,X_n @@ -505,7 +480,38 @@ The fit to the normal density is already tight and can be further improved by in ## Ex 1 -As the reader to rerun the last simulation and experiment with other specifications of $F$ that have finite second moment, making sure that they +Repeat the simulation in (TODO: Add a reference) with [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution). + + +Solution: + +```python +# Set parameters +n = 250 # Choice of n +k = 1_000_000 # Number of draws of Y_n +distribution = st.beta(2,2) # Exponential distribution, λ = 1/2 +μ, σ = distribution.mean(), distribution.std() + +# Draw underlying RVs. Each row contains a draw of X_1,..,X_n +data = distribution.rvs((k, n)) +# Compute mean of each row, producing k draws of \bar X_n +sample_means = data.mean(axis=1) +# Generate observations of Y_n +Y = np.sqrt(n) * (sample_means - μ) + +# Plot +fig, ax = plt.subplots(figsize=(10, 6)) +xmin, xmax = -3 * σ, 3 * σ +ax.set_xlim(xmin, xmax) +ax.hist(Y, bins=60, alpha=0.4, density=True) +xgrid = np.linspace(xmin, xmax, 200) +ax.plot(xgrid, st.norm.pdf(xgrid, scale=σ), 'k-', lw=2, label='$N(0, \sigma^2)$') +ax.legend() + +plt.show() +``` + +## Ex 2 Although NumPy doesn't give us a `bernoulli` function, we can generate a draw of $X$ using NumPy via From a0fdcaea1edc22cc690aeadc621116528bf8ce55 Mon Sep 17 00:00:00 2001 From: Humphrey Yang Date: Wed, 1 Feb 2023 12:17:35 +1100 Subject: [PATCH 05/12] update markdown --- in-work/lln_clt.md | 247 +++++++++++++++++++++++---------------------- 1 file changed, 128 insertions(+), 119 deletions(-) diff --git a/in-work/lln_clt.md b/in-work/lln_clt.md index f9c4c5ac5..3ea4e4902 100644 --- a/in-work/lln_clt.md +++ b/in-work/lln_clt.md @@ -1,12 +1,11 @@ --- -jupyter: - jupytext: +jupytext: text_representation: - extension: .md - format_name: markdown - format_version: '1.3' - jupytext_version: 1.14.4 - kernelspec: + extension: .md + format_name: myst + format_version: 0.13 + jupytext_version: 1.14.4 +kernelspec: display_name: Python 3 (ipykernel) language: python name: python3 @@ -34,14 +33,13 @@ Some of these extensions are presented as exercises. We'll need the following imports: -```python +```{code-cell} ipython3 import matplotlib.pyplot as plt import random import numpy as np import scipy.stats as st ``` - ## Relationships @@ -78,9 +76,8 @@ $$ $$ We can generate a draw of $X$ with `scipy.stats` (imported as `st`) as follows: - -```python +```{code-cell} ipython3 p = 0.8 X = st.bernoulli.rvs(p) print(X) @@ -90,15 +87,15 @@ In this setting, the LLN tells us if we flip the coin many times, the fraction o Let's check this: -```python +```{code-cell} ipython3 n = 1_000_000 X_draws = st.bernoulli.rvs(p, size=n) -print(X_draws.mean()) # count the number of 1's and divide by n +print(X_draws.mean()) # count the number of 1's and divide by n ``` If we change $p$ the claim still holds: -```python +```{code-cell} ipython3 p = 0.3 X_draws = st.bernoulli.rvs(p, size=n) print(X_draws.mean()) @@ -127,7 +124,8 @@ Thus, the LLN tells us that This is exactly what we illustrated in the code above. - ++++ {"jp-MarkdownHeadingCollapsed": true, "tags": []} + (lln_ksl)= ### Statement of the LLN @@ -137,13 +135,13 @@ The traditional version of the law of large numbers concerns independent and ide Let $X_1, \ldots, X_n$ be independent and identically distributed random variables. -These random variables can be continuous or discrete. +This random variables can be continuous or discrete. -For simplicity we will assume they are continuous, and we let $f$ denote their density function, so that, for any $i$ in $\{1, \ldots, n\}$ +For simplicity we will assume they are continuous and we let $f$ denote their density function, so that, for any $i$ in $\{1, \ldots, n\}$ $$ - \mathbb P\{a \leq X_i \leq b\} = \int_a^b f(x) dx + \mathbb P\{a \leq X_i \leq b\} = \int_a^b f(x) dx $$ (For the discrete case, we need to replace densities with probability mass functions and integrals with sums.) @@ -151,7 +149,7 @@ $$ Let $\mu$ denote the common mean of this sample: $$ - \mu := \mathbb E X = \int_{-\infty}^{\infty} x f(dx) + \mu := \mathbb E X = \int_{-\infty}^{\infty} x f(dx) $$ In addition, let @@ -181,9 +179,9 @@ Let's also imagine that we can generate infinite sequences so that the statement In this setting, {eq}`lln_as` should be interpreted as meaning that the probability of the computer producing a sequence where $\bar X_n \to \mu$ fails to occur is zero. - - ++++ {"tags": []} + ### Illustration ```{index} single: Law of Large Numbers; Illustration @@ -216,38 +214,37 @@ Moreover, if we repeat the exercise with a larger value of $n$, we should see th This is, in essence, what the LLN is telling us. Let's run some simulations to visualize LLN - -```python +```{code-cell} ipython3 def generate_histogram(X_distribution, n, m): - fig, ax = plt.subplots(figsize=(10, 6)) - - def draw_means(X_distribution, n): - - # Step 3: Generate n draws: X_1, ..., X_n - X_samples = X_distribution.rvs(size=n) - - # Step 4: Calculate the sample mean - return np.mean(X_samples) - - # Step 5: Loop m times - sample_means = [draw_means(X_distribution, n) for i in range(m)] - print(f'The mean of sample mean is {round(np.mean(sample_means),2)}') - - # Generate a histogram - ax.hist(sample_means, bins=30, alpha=0.5, density=True) - mu = X_distribution.mean() - if not np.isnan(mu): - ax.axvline(x=mu, ls="--", lw=3, label=fr"$\mu = {mu}$") - - ax.set_xlim(min(sample_means), max(sample_means)) - ax.set_xlabel(r'$\bar x$') - ax.set_ylabel('Density') - ax.legend() - plt.show() + fig, ax = plt.subplots(figsize=(10, 6)) + + def draw_means(X_distribution, n): + + # Step 3: Generate n draws: X_1, ..., X_n + X_samples = X_distribution.rvs(size=n) + + # Step 4: Calculate sample mean + return np.mean(X_samples) + + # Step 5: Loop m times + sample_means = [draw_means(X_distribution, n) for i in range(m)] + print(f'The mean of sample mean is {round(np.mean(sample_means),2)}') + + # Generate a histogram + ax.hist(sample_means, bins=30, alpha=0.5, density=True) + mu = X_distribution.mean() + if not np.isnan(mu): + ax.axvline(x=mu, ls="--", lw=3, label=fr"$\mu = {mu}$") + + ax.set_xlim(min(sample_means), max(sample_means)) + ax.set_xlabel(r'$\bar x$') + ax.set_ylabel('Density') + ax.legend() + plt.show() ``` -```python +```{code-cell} ipython3 #Step 1: Pick some distribution to draw each $X_i$ from #Step 2: Set $n$ to some large number generate_histogram(st.norm(loc=5, scale=2), n=50_000, m=1000) @@ -257,40 +254,41 @@ We can see that the distribution of $\bar X$ is clustered around $\mathbb E X$ a We can increase values for `n` and `m` to see how the distribution changes by slightly changing the code to see the changes with an increasing $n$ -```python +```{code-cell} ipython3 def generate_multiple_hist(X_distribution, ns, m, log_scale=False): - _, ax = plt.subplots(figsize=(10, 6)) - - def draw_means(X_distribution, n): - X_samples = X_distribution.rvs(size=n) - return np.mean(X_samples) - - for n in ns: - sample_means = [draw_means(X_distribution, n) for i in range(m)] - if log_scale: - plt.xscale('symlog') - ax.hist(sample_means, bins=60, alpha=0.4, density=True, label=fr'$n = {n}$') - - mu = X_distribution.mean() - if not np.isnan(mu): - ax.axvline(x=mu, ls="--", lw=3, label=fr"$\mu = {mu}$") - - ax.set_xlim(min(sample_means), max(sample_means)) - ax.set_xlabel(r'$\bar x$') - ax.set_ylabel('Density') - ax.set(title=fr'$n = {n}, m = {m}$') - ax.legend() - plt.show() + _, ax = plt.subplots(figsize=(10, 6)) + + def draw_means(X_distribution, n): + X_samples = X_distribution.rvs(size=n) + return np.mean(X_samples) + + for n in ns: + sample_means = [draw_means(X_distribution, n) for i in range(m)] + if log_scale: + plt.xscale('symlog') + ax.hist(sample_means, bins=60, alpha=0.4, density=True, label=fr'$n = {n}$') + + mu = X_distribution.mean() + if not np.isnan(mu): + ax.axvline(x=mu, ls="--", lw=3, label=fr"$\mu = {mu}$") + + ax.set_xlim(min(sample_means), max(sample_means)) + ax.set_xlabel(r'$\bar x$') + ax.set_ylabel('Density') + ax.set(title=fr'$n = {n}, m = {m}$') + ax.legend() + plt.show() ``` -```python +```{code-cell} ipython3 generate_multiple_hist(st.norm(loc=5, scale=2), ns=[20_000, 50_000, 100_000], m=10_000) ``` -We see that from the histogram that it gradually converges to $\mu$. +We see that the histogram gradually converge to $\mu$. You can imagine the result when extrapolating this trend for $n \to \infty$. ++++ ## Breaking the LLN @@ -300,57 +298,59 @@ As indicated by {eq}`lln_as`, LLN can break when $\mathbb E |X|$ is not finite o We can demonstrate this using a simple simulation using a [Cauchy distribution](https://en.wikipedia.org/wiki/Cauchy_distribution) for which it does not have a well-defined $\mu$. ++++ We lost the convergence we have seen before with normal distribution -```python +```{code-cell} ipython3 fig, axes = plt.subplots(1, 2, figsize=(15, 6)) def scattered_mean(distribution, burn_in, n, jump, ax, title, color, ylog=False): - - #Set a jump to reduce simulation complexity - sample_means = [np.mean(distribution.rvs(size=i)) - for i in range(burn_in, n+1, jump)] - - ax.scatter(range(burn_in, n+1, jump), sample_means, s=10, c=color) - - #Change the y-axis to log scale if necessary - if ylog: - ax.set_yscale("symlog") - ax.set_title(title, size=10) - ax.set_xlabel(r"$n$", size=12) - ax.set_ylabel(r"$\bar x$", size=12) - yabs_max = max(ax.get_ylim(), key=abs) - ax.set_ylim(ymin=-yabs_max, ymax=yabs_max) - return ax + + #Set a jump to reduce simulation complexity + sample_means = [np.mean(distribution.rvs(size=i)) + for i in range(burn_in, n+1, jump)] + + ax.scatter(range(burn_in, n+1, jump), sample_means, s=10, c=color) + + #Change the y-axis to log scale if necessory + if ylog: + ax.set_yscale("symlog") + ax.set_title(title, size=10) + ax.set_xlabel(r"$n$", size=12) + ax.set_ylabel(r"$\bar x$", size=12) + yabs_max = max(ax.get_ylim(), key=abs) + ax.set_ylim(ymin=-yabs_max, ymax=yabs_max) + return ax scattered_mean(distribution=st.cauchy(), - burn_in=1000, - n=1_000_000, - ax=axes[0], - jump=2000, - title="Cauchy Distribution", - color='#1f77b4', - ylog=True) + burn_in=1000, + n=1_000_000, + ax=axes[0], + jump=2000, + title="Cauchy Distribution", + color='#1f77b4', + ylog=True) scattered_mean(distribution=st.norm(), - burn_in=1000, - n=1_000_000, - ax=axes[1], - jump=2000, - title="Normal Distribution", - color='#ff7f0e') + burn_in=1000, + n=1_000_000, + ax=axes[1], + jump=2000, + title="Normal Distribution", + color='#ff7f0e') fig.suptitle('Sample Mean with Different Sample Size') plt.show() ``` -We can see that, unlike normal distribution, the Cauchy distribution does not have the convergence that LLN implies. +We can see that unlike normal distribution, Cauchy distribution does not have a convergence that LLN implies. It is also not hard to conjecture that LLN can be broken when the IID assumption is violated. ++++ -Let's go through a very simple example where LLN fails with the IID violated: +Let's go through a very simple example where LLN fails with IID violated: Assume @@ -367,10 +367,10 @@ $$ We can then see that $$ -\bar X_n := \frac{1}{n} \sum_{t=1}^n X_i = X_1 \sim \mathcal{N}(0,1) +\bar X_n := \frac{1}{n} \sum_{t=1}^n X_i = X_1 \sim \mathcal{N}(0,1) $$ -Therefore, the distribution of the mean of X follows $\mathcal{N}(0,1)$. +Therefore, the distribution of mean of X follows $\mathcal{N}(0,1)$. However, @@ -384,6 +384,7 @@ which violates {eq}`exp`, and thus breaks LLN. Although in this case, the violation of IID breaks LLN, it is not always the case for correlated data (TODO: Link to MC Lecture) ``` ++++ ## CLT @@ -423,7 +424,8 @@ The striking implication of the CLT is that for **any** distribution with finite second moment, the simple operation of adding independent copies **always** leads to a Gaussian curve. - ++++ {"tags": []} + ### Simulation 1 Since the CLT seems almost magical, running simulations that verify its implications is one good way to build intuition. @@ -441,13 +443,12 @@ $F(x) = 1 - e^{- \lambda x}$. (Please experiment with other choices of $F$, but remember that, to conform with the conditions of the CLT, the distribution must have a finite second moment.) (sim_one)= - -```python +```{code-cell} ipython3 # Set parameters -n = 250 # Choice of n -k = 1_000_000 # Number of draws of Y_n -distribution = st.expon(2) # Exponential distribution, λ = 1/2 +n = 250 # Choice of n +k = 1_000_000 # Number of draws of Y_n +distribution = st.expon(2) # Exponential distribution, λ = 1/2 μ, σ = distribution.mean(), distribution.std() # Draw underlying RVs. Each row contains a draw of X_1,..,X_n @@ -473,23 +474,27 @@ plt.show() The fit to the normal density is already tight and can be further improved by increasing `n`. ++++ ## Exercises ++++ ## Ex 1 ++++ Repeat the simulation in (TODO: Add a reference) with [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution). ++++ Solution: -```python +```{code-cell} ipython3 # Set parameters -n = 250 # Choice of n -k = 1_000_000 # Number of draws of Y_n -distribution = st.beta(2,2) # Exponential distribution, λ = 1/2 +n = 250 # Choice of n +k = 1_000_000 # Number of draws of Y_n +distribution = st.beta(2,2) # Exponential distribution, λ = 1/2 μ, σ = distribution.mean(), distribution.std() # Draw underlying RVs. Each row contains a draw of X_1,..,X_n @@ -513,10 +518,11 @@ plt.show() ## Ex 2 ++++ Although NumPy doesn't give us a `bernoulli` function, we can generate a draw of $X$ using NumPy via -```python +```{code-cell} ipython3 U = np.random.rand() X = 1 if U < p else 0 print(X) @@ -524,9 +530,11 @@ print(X) Explain why this provides a random variable $X$ with the right distribution. ++++ Solution: ++++ We can write $X$ as $X = \mathbf 1\{U < p\}$ where $\mathbf 1$ is the [indicator function](https://en.wikipedia.org/wiki/Indicator_function) (i.e., 1 if the statement is true and zero otherwise). @@ -538,6 +546,7 @@ $$ This means that $X = \mathbf 1\{U < p\}$ has the right distribution. ++++ ```{solution-end} ``` From 5b7674fd922b8145cd4d2d2acb5601ebc0d9a0e2 Mon Sep 17 00:00:00 2001 From: Humphrey Yang Date: Thu, 2 Feb 2023 21:08:12 +1100 Subject: [PATCH 06/12] add ex3 --- in-work/lln_clt.ipynb | 22 ++++++++++++++++++++-- 1 file changed, 20 insertions(+), 2 deletions(-) diff --git a/in-work/lln_clt.ipynb b/in-work/lln_clt.ipynb index 914efe702..57a85e431 100644 --- a/in-work/lln_clt.ipynb +++ b/in-work/lln_clt.ipynb @@ -560,7 +560,7 @@ "which violates {eq}`exp`, and thus breaks LLN.\n", "\n", "```{note}\n", - "Although in this case, the violation of IID breaks LLN, it is not always the case for correlated data (TODO: Link to MC Lecture)\n", + "Although in this case, the violation of IID breaks LLN, it is not always the case for correlated data (TODO: Link to Exercise)\n", "```" ] }, @@ -708,7 +708,7 @@ "id": "40206358-6c49-4a4c-9c81-a6ae70d9c8fe", "metadata": {}, "source": [ - "Repeat the simulation in (TODO: Add a reference) with [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution). " + "Repeat the simulation in (TODO: Add a reference to simulation one) with [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution). " ] }, { @@ -830,6 +830,24 @@ "This means that $X = \\mathbf 1\\{U < p\\}$ has the right distribution." ] }, + { + "cell_type": "markdown", + "id": "c03dd62e-994e-4976-8e6e-bcb196da9013", + "metadata": {}, + "source": [ + "## Ex 3" + ] + }, + { + "cell_type": "markdown", + "id": "79776f08-aeda-4642-bdfe-1931548e1f3f", + "metadata": {}, + "source": [ + "We mentioned above that it is possible for LLN to hold when IID is violated.\n", + "\n", + "\n" + ] + }, { "cell_type": "markdown", "id": "00e14b9a", From f4179ba507bf24087162c0f3a1de7599db503006 Mon Sep 17 00:00:00 2001 From: Humphrey Yang Date: Fri, 3 Feb 2023 09:27:28 +1100 Subject: [PATCH 07/12] with variance --- in-work/lln_clt.ipynb | 157 +++++++++++++++++++++++++++++++++++++++++- 1 file changed, 156 insertions(+), 1 deletion(-) diff --git a/in-work/lln_clt.ipynb b/in-work/lln_clt.ipynb index 57a85e431..4e836c64f 100644 --- a/in-work/lln_clt.ipynb +++ b/in-work/lln_clt.ipynb @@ -367,7 +367,7 @@ "source": [ "We can see that the distribution of $\\bar X$ is clustered around $\\mathbb E X$ as expected.\n", "\n", - "We can increase values for `n` and `m` to see how the distribution changes by slightly changing the code to see the changes with an increasing $n$" + "We can vary values for `n` to see how the distribution changes" ] }, { @@ -845,9 +845,156 @@ "source": [ "We mentioned above that it is possible for LLN to hold when IID is violated.\n", "\n", + "Let's investigate this claim further.\n", + "\n", + "Assume we have a AR(1) process as below:\n", + "\n", + "$$\n", + "X_{t+1} = \\alpha + \\beta X_t + \\sigma \\epsilon _{t+1}\n", + "$$\n", + "\n", + "$$\n", + "X_0 \\sim \\mathcal{N}(\\frac{\\alpha}{1-\\beta}, \\frac{\\alpha^2}{1-\\beta^2})\n", + "$$\n", + "\n", + "where $\\epsilon_t \\sim \\mathcal{N}(0,1)$\n", + "\n", + "Show LLN holds using simulations with $\\alpha = 0.8$, $\\beta = 0.2$." + ] + }, + { + "cell_type": "markdown", + "id": "694d0c2e-dd9b-402b-a4f6-ff576cf15b1f", + "metadata": {}, + "source": [ + "Solution:\n", + "\n", + "Let's verify the expectation and variance of this AR(1) process using pen and paper first.\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mathbb E X_{t+1} &= \\alpha + \\beta \\mathbb E X_t \\\\\n", + "&= \\alpha + \\beta \\frac{\\alpha}{1-\\beta} \\\\\n", + "&= \\frac{\\alpha}{1-\\beta}\n", + "\\end{aligned}\n", + "$$ \n", + "\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mathbb Var X_t &= \\beta^2 \\mathbb Var X_{t-1} + \\sigma^2\\\\\n", + "\\end{aligned}\n", + "$$ \n", "\n" ] }, + { + "cell_type": "code", + "execution_count": null, + "id": "deccd68a-e528-4be3-bf0c-14b1581680c7", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Simulated Variance is 104.16666666666667\n" + ] + } + ], + "source": [ + "import scipy.stats as st\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "σ = 10\n", + "α = 0.8\n", + "β = 0.2\n", + "n = 100_000\n", + "\n", + "var = np.ones(n)\n", + "var[0] = α**2/(1-β**2)\n", + "for t in range(n-1):\n", + " var[t+1] = β**2*var[t]+σ**2\n", + "plt.plot(var)\n", + "plt.show()\n", + "\n", + "print(f'Simulated Variance is {var[-1]}')" + ] + }, + { + "cell_type": "markdown", + "id": "62e5c20e-1644-45ae-b178-a883b726a198", + "metadata": {}, + "source": [ + "Note that\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mathbb Var X_t &= \\beta^2 \\mathbb Var X_{t-1} + \\sigma^2\\\\\n", + "\\end{aligned}\n", + "$$ \n", + "\n", + "has a stable fixed point.\n", + "\n", + "\n", + "Thus, assuming $\\mathbb Var X_t^* = X_{t-1}^*$, we have\n", + "$$\n", + "\\begin{aligned}\n", + "\\mathbb Var X_t &= \\frac{\\sigma^2}{1-\\beta^2}\\\\\n", + "\\end{aligned}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "622c8cdb-e830-4ef3-9b1a-a273b589d79c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(10, 6))\n", + "x = np.ones(n)\n", + "x[0] = st.norm.rvs(α/(1-β), α**2/(1-β**2))\n", + "ϵ = st.norm.rvs(size=n+1)\n", + "means = np.ones(n)\n", + "for t in range(n-1):\n", + " x[t+1] = α + β * x[t] + σ * ϵ[t+1]\n", + " means[t+1] = np.mean(x[:t])\n", + "\n", + "\n", + "ax.scatter(range(n), means, s=10, alpha=0.5)\n", + "\n", + "ax.set_xlabel(r\"$n$\", size=12)\n", + "ax.set_ylabel(r\"$\\bar x$\", size=12)\n", + "yabs_max = max(ax.get_ylim(), key=abs)\n", + "ax.axhline(y=α/(1-β), ls=\"--\", lw=3, label=r\"$\\mu = \\frac{\\alpha}{1-\\beta}$\",color = 'black')\n", + "\n", + "plt.legend()\n", + "plt.show()" + ] + }, { "cell_type": "markdown", "id": "00e14b9a", @@ -856,6 +1003,14 @@ "```{solution-end}\n", "```" ] + }, + { + "cell_type": "markdown", + "id": "d40afcf5-6106-4b82-bfd9-7efce3cee066", + "metadata": {}, + "source": [ + "We see the convergence in $\\bar x$ to $\\mu$ even when IID assumption is violated." + ] } ], "metadata": { From ed20a2352ac20b032822c79e8ecd29d8fc35151e Mon Sep 17 00:00:00 2001 From: Humphrey Yang Date: Fri, 3 Feb 2023 11:10:09 +1100 Subject: [PATCH 08/12] update exercise --- in-work/lln_clt.ipynb | 387 +++++++++++++++++++----------------------- in-work/lln_clt.md | 287 +++++++++++++++++++++---------- 2 files changed, 367 insertions(+), 307 deletions(-) diff --git a/in-work/lln_clt.ipynb b/in-work/lln_clt.ipynb index 4e836c64f..44e60072e 100644 --- a/in-work/lln_clt.ipynb +++ b/in-work/lln_clt.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "abbf8725", + "id": "7d6e1b22", "metadata": {}, "source": [ "## LLN and CLT\n", @@ -31,7 +31,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "85a6731b", + "id": "a8a9c791", "metadata": {}, "outputs": [], "source": [ @@ -43,7 +43,7 @@ }, { "cell_type": "markdown", - "id": "406e1374", + "id": "27b198f3", "metadata": {}, "source": [ "## Relationships\n", @@ -87,7 +87,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "821a73c3", + "id": "e908d632", "metadata": {}, "outputs": [ { @@ -106,7 +106,7 @@ }, { "cell_type": "markdown", - "id": "c3146d09", + "id": "5458e7ef", "metadata": {}, "source": [ "In this setting, the LLN tells us if we flip the coin many times, the fraction of heads that we see will be close to $p$.\n", @@ -117,26 +117,26 @@ { "cell_type": "code", "execution_count": 3, - "id": "d95827fd", + "id": "9815c7fc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "0.799764\n" + "0.799818\n" ] } ], "source": [ "n = 1_000_000\n", "X_draws = st.bernoulli.rvs(p, size=n)\n", - "print(X_draws.mean()) # count the number of 1's and divide by n" + "print(X_draws.mean()) # count the number of 1's and divide by n" ] }, { "cell_type": "markdown", - "id": "e95b76a1", + "id": "eb4e5a32", "metadata": {}, "source": [ "If we change $p$ the claim still holds:" @@ -145,14 +145,14 @@ { "cell_type": "code", "execution_count": 4, - "id": "404dbe87", + "id": "9810b20f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "0.299568\n" + "0.299727\n" ] } ], @@ -164,7 +164,7 @@ }, { "cell_type": "markdown", - "id": "78db68f3", + "id": "70bcf799", "metadata": {}, "source": [ "Let's connect this to the discussion above, where we said the sample average converges to the \"population mean\".\n", @@ -193,7 +193,7 @@ }, { "cell_type": "markdown", - "id": "3faf5ee2", + "id": "76ab8554", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] @@ -208,13 +208,13 @@ "\n", "Let $X_1, \\ldots, X_n$ be independent and identically distributed random variables.\n", "\n", - "This random variables can be continuous or discrete.\n", + "These random variables can be continuous or discrete.\n", "\n", "For simplicity we will assume they are continuous and we let $f$ denote their density function, so that, for any $i$ in $\\{1, \\ldots, n\\}$\n", "\n", "\n", "$$ \n", - " \\mathbb P\\{a \\leq X_i \\leq b\\} = \\int_a^b f(x) dx\n", + " \\mathbb P\\{a \\leq X_i \\leq b\\} = \\int_a^b f(x) dx\n", "$$\n", "\n", "(For the discrete case, we need to replace densities with probability mass functions and integrals with sums.)\n", @@ -222,7 +222,7 @@ "Let $\\mu$ denote the common mean of this sample:\n", "\n", "$$\n", - " \\mu := \\mathbb E X = \\int_{-\\infty}^{\\infty} x f(dx)\n", + " \\mu := \\mathbb E X = \\int_{-\\infty}^{\\infty} x f(dx)\n", "$$\n", "\n", "In addition, let\n", @@ -256,7 +256,7 @@ }, { "cell_type": "markdown", - "id": "72ef82c2", + "id": "ebc20e87", "metadata": { "tags": [] }, @@ -298,42 +298,42 @@ { "cell_type": "code", "execution_count": 5, - "id": "9299240a", + "id": "ced10491", "metadata": {}, "outputs": [], "source": [ "def generate_histogram(X_distribution, n, m):\n", - " fig, ax = plt.subplots(figsize=(10, 6))\n", - "\n", - " def draw_means(X_distribution, n):\n", - "\n", - " # Step 3: Generate n draws: X_1, ..., X_n\n", - " X_samples = X_distribution.rvs(size=n)\n", - "\n", - " # Step 4: Calculate sample mean\n", - " return np.mean(X_samples)\n", - " \n", - " # Step 5: Loop m times\n", - " sample_means = [draw_means(X_distribution, n) for i in range(m)]\n", - " print(f'The mean of sample mean is {round(np.mean(sample_means),2)}')\n", - " \n", - " # Generate a histogram\n", - " ax.hist(sample_means, bins=30, alpha=0.5, density=True)\n", - " mu = X_distribution.mean()\n", - " if not np.isnan(mu):\n", - " ax.axvline(x=mu, ls=\"--\", lw=3, label=fr\"$\\mu = {mu}$\")\n", - " \n", - " ax.set_xlim(min(sample_means), max(sample_means))\n", - " ax.set_xlabel(r'$\\bar x$')\n", - " ax.set_ylabel('Density')\n", - " ax.legend()\n", - " plt.show()" + " fig, ax = plt.subplots(figsize=(10, 6))\n", + "\n", + " def draw_means(X_distribution, n):\n", + "\n", + " # Step 3: Generate n draws: X_1, ..., X_n\n", + " X_samples = X_distribution.rvs(size=n)\n", + "\n", + " # Step 4: Calculate the sample mean\n", + " return np.mean(X_samples)\n", + " \n", + " # Step 5: Loop m times\n", + " sample_means = [draw_means(X_distribution, n) for i in range(m)]\n", + " print(f'The mean of sample mean is {round(np.mean(sample_means),2)}')\n", + " \n", + " # Generate a histogram\n", + " ax.hist(sample_means, bins=30, alpha=0.5, density=True)\n", + " mu = X_distribution.mean()\n", + " if not np.isnan(mu):\n", + " ax.axvline(x=mu, ls=\"--\", lw=3, label=fr\"$\\mu = {mu}$\")\n", + " \n", + " ax.set_xlim(min(sample_means), max(sample_means))\n", + " ax.set_xlabel(r'$\\bar x$')\n", + " ax.set_ylabel('Density')\n", + " ax.legend()\n", + " plt.show()" ] }, { "cell_type": "code", "execution_count": 6, - "id": "0b0da74f-1f3d-4b75-bb4a-86c85c4539bb", + "id": "8f8b460c", "metadata": {}, "outputs": [ { @@ -345,7 +345,7 @@ }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -362,7 +362,7 @@ }, { "cell_type": "markdown", - "id": "8dd3b5c4-e6b5-4df6-82e0-5b1d96e06f82", + "id": "4e20ee45", "metadata": {}, "source": [ "We can see that the distribution of $\\bar X$ is clustered around $\\mathbb E X$ as expected.\n", @@ -373,44 +373,44 @@ { "cell_type": "code", "execution_count": 7, - "id": "597a28c8-046e-44d4-b4ce-4bf1d580601c", + "id": "94b05492", "metadata": {}, "outputs": [], "source": [ "def generate_multiple_hist(X_distribution, ns, m, log_scale=False):\n", - " _, ax = plt.subplots(figsize=(10, 6))\n", - "\n", - " def draw_means(X_distribution, n):\n", - " X_samples = X_distribution.rvs(size=n)\n", - " return np.mean(X_samples)\n", - " \n", - " for n in ns:\n", - " sample_means = [draw_means(X_distribution, n) for i in range(m)]\n", - " if log_scale:\n", - " plt.xscale('symlog')\n", - " ax.hist(sample_means, bins=60, alpha=0.4, density=True, label=fr'$n = {n}$')\n", - " \n", - " mu = X_distribution.mean()\n", - " if not np.isnan(mu):\n", - " ax.axvline(x=mu, ls=\"--\", lw=3, label=fr\"$\\mu = {mu}$\")\n", - " \n", - " ax.set_xlim(min(sample_means), max(sample_means)) \n", - " ax.set_xlabel(r'$\\bar x$')\n", - " ax.set_ylabel('Density')\n", - " ax.set(title=fr'$n = {n}, m = {m}$')\n", - " ax.legend()\n", - " plt.show()" + " _, ax = plt.subplots(figsize=(10, 6))\n", + "\n", + " def draw_means(X_distribution, n):\n", + " X_samples = X_distribution.rvs(size=n)\n", + " return np.mean(X_samples)\n", + " \n", + " for n in ns:\n", + " sample_means = [draw_means(X_distribution, n) for i in range(m)]\n", + " if log_scale:\n", + " plt.xscale('symlog')\n", + " ax.hist(sample_means, bins=60, alpha=0.4, density=True, label=fr'$n = {n}$')\n", + " \n", + " mu = X_distribution.mean()\n", + " if not np.isnan(mu):\n", + " ax.axvline(x=mu, ls=\"--\", lw=3, label=fr\"$\\mu = {mu}$\")\n", + " \n", + " ax.set_xlim(min(sample_means), max(sample_means)) \n", + " ax.set_xlabel(r'$\\bar x$')\n", + " ax.set_ylabel('Density')\n", + " ax.set(title=fr'$n = {n}, m = {m}$')\n", + " ax.legend()\n", + " plt.show()" ] }, { "cell_type": "code", "execution_count": 8, - "id": "7dbed08d-3560-4f6d-8bb9-7c3ee75bab43", + "id": "81b7b7c0", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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" ] @@ -425,17 +425,17 @@ }, { "cell_type": "markdown", - "id": "f8c6e4b4-344b-497e-bc71-ecac322be3c8", + "id": "befa85ff", "metadata": {}, "source": [ - "We see that the histogram gradually converge to $\\mu$.\n", + "We see that the histogram gradually converges to $\\mu$.\n", "\n", "You can imagine the result when extrapolating this trend for $n \\to \\infty$." ] }, { "cell_type": "markdown", - "id": "22987bd7", + "id": "e42e4d6d", "metadata": {}, "source": [ "## Breaking the LLN\n", @@ -449,21 +449,21 @@ }, { "cell_type": "markdown", - "id": "dddea715-be50-4d63-82e7-b51115b2c9cf", + "id": "e44f190b", "metadata": {}, "source": [ - "We lost the convergence we have seen before with normal distribution " + "We lost the convergence we have seen before with normal distribution" ] }, { "cell_type": "code", "execution_count": 9, - "id": "dda56a48-d06c-4ed4-9c7e-180d843d1d63", + "id": "68405e18", "metadata": {}, "outputs": [ { "data": { - "image/png": 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XSbZBfI5Wr15d9nyWWshE7rzdvn277PsQ9oswd56YeP5KOWrbQ8mhQ4cwaNAgJCcnY8mSJQHnstbzm4iIKNIwjCMiIrJItWrVMHXqVDz77LPYuXMnAGD16tU4dOgQ1q5dG7Bipdr8beEoLS2VvK1169ayj0lISEBMTAzWr1+PuLi4oN9L3aZk9OjRePTRR/Hiiy/iySefVHzdhg0bYsWKFZK/F1Z4tHI7XnnllXjkkUfwxRdfYNWqVZg6darv9s8++wwtWrTw/exEf/zxBz7//HO0atUKycnJhjxnQkICAOD555+XXTVWHLL5V3kJz2HkMWaUmJgYTJw4EY899pjvvN25cye2b9+OhQsX4rbbbvPdd9++faa1Q+68lQolBcJ+ef/9931Ve+GS2h5yKioqcPXVV+PcuXNYvnw54uPjg9qn5fwmIiKKNAzjiIiITFBSUhJU+QOcH74mVCQJgYQ4aHjppZdMa9ubb74ZMERww4YNOHDggOLE9tdeey1mzpyJn3/+GTfeeGPYbbjwwgvx97//Hd9//31AmCH1uu+88w7Onj2L7t27y97Pyu3YrVs31KtXD7m5uSgtLUX//v0BeCvmZs2ahXfffRcXX3yxatWZ0FYrJ6k/e/Ys7r33Xhw7dgwzZsww7Hl79uyJCy64AN999x3uvffekJ7D6GMM0L+N5c7bQ4cOoaKiAl27dgVgz3n79ttvIycnx/faBw4cwIYNG3DrrbfKPmbgwIGoWrUqfvjhh6BhwVpo3R5STp06hezsbPz000/48ssvJYNfrec3ERFRpGEYR0REZIKBAwciOTkZgwcPRrt27XDu3Dls27YNzzzzDOrUqYMHHngAgHe+tvr162PcuHGYOnUqqlWrhjfffFNx6Fm4CgoKMGbMGNxwww04ePAgHn74YVx44YUYP3687GN69uyJu+66C7fffjsKCgpwxRVXoHbt2igpKcGXX36Jjh074q9//auudsycOVP1PiNHjsSbb76Jq6++Gg888AC6deuGatWqobi4GGvWrMF1112H7OxsS7djbGwsevfujWXLlqFFixZo1aoVAO82iouLw6pVq3D//ferPk/Hjh0BAM899xxuu+02VKtWDW3btjWsGuiXX37B119/DY/HgxMnTmDnzp14/fXXsX37dkycOBFjx4415HUAoE6dOnj++edx22234fjx4xg+fDgaN26MI0eOYPv27Thy5Ajmz5+v+BxmHGOtWrVCzZo18eabbyItLQ116tRB06ZNZYPSu+66C7/++iuGDRuGDh06IDY2Ft9//z2effZZVKlSBZMmTQIAtGvXDq1atcLkyZPh8XjQoEEDLFu2LGBFXaMdPnwY2dnZGDt2LMrLyzF16lTUqFEDU6ZMkX1M8+bN8dhjj+Hhhx/Gjz/+iEGDBqF+/fr45ZdfsGnTJtSuXVtxOLXW7SFl4sSJWL16NZ566in89ttv+Prrr32/a9SoEVq1aqX5/CYiIoo0DOOIiIhM8M9//hMfffQRnn32WZSUlKCyshJNmjTBVVddhSlTpvjmX2rYsCH+7//+Dw8++CBuueUW1K5dG9dddx0WL16MLl26mNK2V155Bf/5z38wcuRIVFZWom/fvnjuueck553z99JLL+Gyyy7DSy+9hLy8PJw7dw5NmzZFz549gybSN0psbCw+/vhjPPfcc/jPf/6DGTNmoGrVqkhOTkbv3r19gZbV2/Gqq67CsmXLAhZpiIuLw+WXX478/HxNizf06dMHU6ZMwaJFi/Dyyy/j3LlzWLNmDfr06WNIG99//328//77qFKlCurUqYNmzZohMzMTL774ouxQ0nDccsstSE1NxezZs3H33XfjxIkTaNy4MTp37ozRo0dreg6jj7FatWrh1VdfxfTp0zFgwACcPn0aU6dOxbRp0yTvf99992Hx4sV4+eWX8fPPP+PkyZNo1KgRMjMz8frrr/u2W7Vq1bBs2TI88MADuPvuu1G1alVcddVV+PzzzwMW3TDSU089hc2bN+P2229HRUUFunXrhnfeeccXBsuZMmUKLr74Yjz33HN4++23UVlZiaSkJFx66aUYN26c4mO1bg8pu3btAgD84x//CPrdbbfdhoULF2o+v4mIiCJNjMfo5bSIiIjIkRYuXIjbb78dmzdv9i0qQUTOtnbtWvTt2xfvvfee4gIZRERE5B7allAiIiIiIiIiIiKisDGMIyIiIiIiIiIisgiHqRIREREREREREVmElXFEREREREREREQWYRhHRERERERERERkEYZxREREREREREREFmEYR0REREREREREZBGGcURERERERERERBZhGEdERERERERERGQRhnFEREREREREREQWYRhHRERERERERERkEYZxREREREREREREFmEYR0REREREREREZBGGcURERERERERERBZhGEdERERERERERGQRhnFEREREREREREQWYRhHRERERERERERkEYZxREREREREREREFmEYR0REREREREREZBGGcURERERERERERBZhGEdERERERERERGQRhnFEREREREREREQWYRhHRERERERERERkEYZxREREREREREREFmEYR0REREREREREZBGGcURERERERERERBZhGEdERERERERERGQRhnFEREREREREREQWYRhHRBEnJiYGH374oW2v37x5c+Tm5hr+vKNHj8b111/v+7lPnz6YMGGC4a8j9VpEREREbrR27VrExMTg119/ddRzifl/fv3pp58QExODbdu2Gf464tciInswjCMiw5SWluK+++5Dy5YtERcXh5SUFAwePBirVq2yu2lhmzZtGmJiYhATE4OqVasiISEBV1xxBXJzc1FZWRlw382bN+Ouu+7S9Lx6grvnnnsOCxcu1NlyZXIf9sx4LSIiInKv0aNHIyYmBjNnzgy4/cMPP0RMTIxNrTJG8+bNfZ/zatasiebNm+PGG2/E6tWrA+7Xo0cPlJSUID4+XvU59QZ3JSUlyMrKCqX5sqZNm4bOnTtb8lpEpA/DOCIyxE8//YSuXbti9erVmD17Nnbs2IEVK1agb9++uOeee+xuniHat2+PkpISFBUVYc2aNbjhhhswY8YM9OjRAydOnPDdr1GjRqhVq5Zhr3v27FmcO3cO8fHxuOCCCwx7XiVWvhYRERG5Q40aNTBr1iyUlZUZ+rynTp0y9PlC8dhjj6GkpAR79uzB66+/jgsuuABXXXUVnnzySd99qlevjqSkJEPDR+G9JyUlIS4uzrDnVWLlaxGRNIZxRGSI8ePHIyYmBps2bcLw4cNx0UUXoX379sjJycHXX3/tu9+cOXPQsWNH1K5dGykpKRg/fjx+++033++lvsHLzc1F8+bNA2579dVX0b59e8TFxaFJkya49957A35/9OhRZGdno1atWmjTpg0+/vhjAIDH40Hr1q3xr3/9K+D+O3fuRJUqVfDDDz/IvseqVasiKSkJTZs2RceOHXHfffdh3bp12LlzJ2bNmuW7n7jabdq0aUhNTUVcXByaNm2K+++/H4B3mOmBAwcwceJE37exALBw4UJccMEF+OSTT3DxxRcjLi4OBw4ckBw6eubMGdx777244IIL0LBhQ/zzn/+Ex+Px/V5qGMIFF1zgq3pr0aIFACA9PR0xMTHo06cPgOBhqpWVlbj//vvRuHFj1KhRA5dffjk2b97s+73w7e+qVauQkZGBWrVqoUePHtizZ4/s9iQiIiJ3ueqqq5CUlIQZM2Yo3u+DDz7wfU5r3rw5nnnmmYDfN2/eHE888QRGjx6N+Ph4jB07NuDzT9u2bVGrVi0MHz4cJ0+exKJFi9C8eXPUr18f9913H86ePet7rjfeeAMZGRmoW7cukpKScNNNN+Hw4cO635vw+NTUVFxxxRVYsGABHnnkETz66KO+zzPiarcDBw5g8ODBqF+/PmrXro327dtj+fLl+Omnn9C3b18AQP369RETE4PRo0cD8H7+u/fee5GTk4OEhAT0798fgPRntu+//x49evRAjRo10L59e6xdu9b3O2F7+fOvUly4cCGmT5+O7du3+z5nCp//xK+1Y8cO9OvXDzVr1kTDhg1x1113BXw+Fz4X/utf/0KTJk3QsGFD3HPPPTh9+rTu7UxEXgzjiChsx48fx4oVK3DPPfegdu3aQb/3/6BQpUoVzJ07Fzt37sSiRYuwevVqPPTQQ7peb/78+bjnnntw1113YceOHfj444/RunXrgPtMnz4dN954I7799ltcffXVuPnmm3H8+HHExMTgjjvuwGuvvRZw/1dffRW9evVCq1atdLWlXbt2yMrKwpIlSyR///777+PZZ5/FSy+9hL179+LDDz9Ex44dAQBLlixBcnKy75vYkpIS3+N+//13zJgxA//+97+xa9cuNG7cWPL5Fy1ahKpVq+Kbb77B3Llz8eyzz+Lf//635vZv2rQJAPD555+jpKRE9n089NBD+OCDD7Bo0SJs3boVrVu3xsCBA3H8+PGA+z388MN45plnUFBQgKpVq+KOO+7Q3BYiIiJyttjYWDz11FN4/vnnUVxcLHmfLVu24MYbb8TIkSOxY8cOTJs2DY888kjQ9BdPP/00OnTogC1btuCRRx4B4P38M3fuXLzzzjtYsWIF1q5di6FDh2L58uVYvnw5/vOf/2DBggV4//33fc9z6tQpPP7449i+fTs+/PBD7N+/3xd8heuBBx6Ax+PBRx99JPn7e+65B5WVlfjiiy+wY8cOzJo1C3Xq1EFKSgo++OADAMCePXtQUlKC5557zvc44fPbV199hZdeekn29f/+97/jwQcfRGFhIXr06IEhQ4bg2LFjmto+YsQIPPjgg76RHSUlJRgxYkTQ/X7//XcMGjQI9evXx+bNm/Hee+/h888/D/qie82aNfjhhx+wZs0aLFq0CAsXLuSUJkRhqGp3A4jI/fbt2wePx4N27dqp3td/wYEWLVrg8ccfx1//+lfk5eVpfr0nnngCDz74IB544AHfbZdeemnAfUaPHo2//OUvAOD70Lhp0yYMGjQIt99+Ox599FFs2rQJ3bp1w+nTp/HGG2/g6aef1twGf+3atcNnn30m+buioiIkJSXhqquuQrVq1ZCamopu3boBABo0aIDY2FjfN7H+Tp8+jby8PHTq1EnxtVNSUvDss88iJiYGbdu2xY4dO/Dss89i7NixmtreqFEjAEDDhg2D2iA4efIk5s+fj4ULF/rmF3n55ZeRn5+PV155BX//+999933yySfRu3dvAMDkyZNxzTXX4M8//0SNGjU0tYeIiIicLTs7G507d8bUqVPxyiuvBP1+zpw5uPLKK30B20UXXYTvvvsOTz/9dEBI1q9fP/ztb3/z/fzll1/i9OnTmD9/vu/L0eHDh+M///kPfvnlF9SpUwcXX3wx+vbtizVr1viCJf8v/lq2bIm5c+eiW7du+O2331CnTp2w3muDBg3QuHFj/PTTT5K/LyoqwrBhw3xftLZs2TLgsQDQuHHjoAq21q1bY/bs2aqvf++992LYsGEAvF9Gr1ixAq+88oqmL7Jr1qyJOnXq+EZ2yHnzzTfxxx9/4PXXX/d9qT5v3jwMHjwYs2bNQmJiIgBvhd+8efMQGxuLdu3a4ZprrsGqVas0f+YkokCsjCOisAnDIrXMn7FmzRr0798fF154IerWrYtbb70Vx44dw8mTJzW91uHDh3Ho0CFceeWVive75JJLfP9fu3Zt1K1b1zdkoUmTJrjmmmvw6quvAgA++eQT/Pnnn7jhhhs0tUHM4/HIvvcbbrgBf/zxB1q2bImxY8di6dKlOHPmjOpzVq9ePeA9yLnssssCXjszMxN79+4NGL4Rrh9++AGnT59Gz549fbdVq1YN3bp1w+7duwPu69/mJk2aAEBIQ0WIiIjIuWbNmoVFixbhu+++C/rd7t27Az4zAEDPnj2DPp9kZGQEPbZWrVoBoxQSExPRvHnzgFAtMTEx4LNFYWEhrrvuOjRr1gx169b1TblRVFQU8vvzp/Q57/7778cTTzyBnj17YurUqfj22281PafUe5eSmZnp+/+qVasiIyMj6LNXuHbv3o1OnToFjG7p2bMnzp07FzDdSPv27REbG+v7uUmTJvyMRxQGhnFEFLY2bdogJiZG9cPBgQMHcPXVV6NDhw744IMPsGXLFrzwwgsA4JtzokqVKgFznvn/DvB+y6dFtWrVAn6OiYnBuXPnfD+PGTMG77zzDv744w+89tprGDFiRMiLLuzevds395pYSkoK9uzZgxdeeAE1a9bE+PHjccUVV6jOsVGzZk1DJgeOiYlR3J5ayIWtUh9O/be78Dv/7U5ERETud8UVV2DgwIH4xz/+EfQ7qc8H4s8iACSnNpH6/Kb0me7kyZMYMGAA6tSpgzfeeAObN2/G0qVLARizKMSxY8dw5MgR2c95Y8aMwY8//ohRo0Zhx44dyMjIwPPPP6/6vFLvXSth26p9ZtZKKWz0v13tszUR6cMwjojC1qBBAwwcOBAvvPCCZIWbMMltQUEBzpw5g2eeeQaXXXYZLrroIhw6dCjgvo0aNUJpaWnAh4tt27b5/r9u3bpo3rw5Vq1aFVabr776atSuXRvz58/Hp59+GvLcZt9//z1WrFjhG0IgpWbNmhgyZAjmzp2LtWvXYuPGjdixYwcAbwVcOFVs/otjCD+3adPG981lo0aNAuai27t3L37//Xffz9WrVwcAxTa0bt0a1atXx5dffum77fTp0ygoKEBaWlrIbSciIiL3mjlzJpYtW4YNGzYE3H7xxRcHfGYAgA0bNuCiiy4KqKwywvfff4+jR49i5syZ6NWrF9q1a2dotdZzzz2HKlWqBC2g5S8lJQXjxo3DkiVL8OCDD+Lll18GoO0zlhr/z3lnzpzBli1bfNPCNGrUCCdOnAj47O3/mVlog9rrX3zxxdi2bVvA83z11VeoUqUKLrroopDbTkTKGMYRkSHy8vJw9uxZdOvWDR988AH27t2L3bt3Y+7cub4S+1atWuHMmTN4/vnn8eOPP+I///kPXnzxxYDn6dOnD44cOYLZs2fjhx9+wAsvvIBPP/004D7Tpk3DM888g7lz52Lv3r3YunWrpm8h/cXGxmL06NGYMmUKWrduHTAMQM6ZM2dQWlqKQ4cOYceOHXj++efRu3dvdO7cOWDeNH8LFy7EK6+8gp07d/rec82aNdGsWTMA3tXEvvjiC/z88884evSorvcAAAcPHkROTg727NmDt99+G88//3zAXHr9+vXDvHnzsHXrVhQUFGDcuHEB32w2btwYNWvWxIoVK/DLL7+gvLw86DVq166Nv/71r/j73/+OFStW4LvvvsPYsWPx+++/484779TdZiIiInK/jh074uabbw76DPbggw9i1apVePzxx/Hf//4XixYtwrx58wLmhzNKamoqqlev7vts+fHHH+Pxxx8P6blOnDiB0tJSHDx4EF988QXuuusuPPHEE3jyySeDFgoTTJgwAStXrsT+/fuxdetWrF692vdFZbNmzRATE4NPPvkER44cCVidVKsXXngBS5cuxffff4977rkHZWVlvi+Qu3fvjlq1auEf//gH9u3bh7feeitoQYXmzZtj//792LZtG44ePYrKysqg17j55ptRo0YN3Hbbbdi5cyfWrFmD++67D6NGjfLNF0dExmMYR0SGaNGiBbZu3Yq+ffviwQcfRIcOHdC/f3+sWrUK8+fPBwB07twZc+bMwaxZs9ChQwe8+eabmDFjRsDzpKWlIS8vDy+88AI6deqETZs2BX14u+2225Cbm4u8vDy0b98e1157Lfbu3au7zXfeeSdOnTqluSpu165daNKkCVJTU9GnTx+8++67mDJlCtavXy87QfAFF1yAl19+GT179sQll1yCVatWYdmyZWjYsCEA4LHHHsNPP/2EVq1a+RZT0OPWW2/FH3/8gW7duuGee+7Bfffdh7vuusv3+2eeeQYpKSm44oorcNNNN+Fvf/tbwHDcqlWrYu7cuXjppZfQtGlTXHfddZKvM3PmTAwbNgyjRo1Cly5dsG/fPqxcuRL169fX3WYiIiKKDI8//njQUMkuXbrg3XffxTvvvIMOHTrg0UcfxWOPPWbYCqf+GjVqhIULF+K9997DxRdfjJkzZ+Jf//pXSM/16KOPokmTJmjdujVGjRqF8vJyrFq1CpMmTZJ9zNmzZ3HPPfcgLS0NgwYNQtu2bX2Lkl144YWYPn06Jk+ejMTExKDVSbWYOXMmZs2ahU6dOmH9+vX46KOPkJCQAMA7MuWNN97A8uXL0bFjR7z99tuYNm1awOOHDRuGQYMGoW/fvmjUqBHefvvtoNeoVasWVq5ciePHj+PSSy/F8OHDceWVV2LevHm620tE2sV4pAbwExFFga+++gp9+vRBcXExv/kjIiIiIiIiSzCMI6KoU1lZiYMHD+Kuu+5CkyZN8Oabb9rdJCIiIiIiIooSHKZKRFHn7bffRtu2bVFeXo7Zs2fb3RwiIiIiIiKKIqyMIyIiIiIiIiIisggr44iIiIiIiIiIiCzCMI6IiIiIiIiIiMgiDOOIiIiIiIiIiIgsUtXuBrjVuXPncOjQIdStWxcxMTF2N4eIiIhcwOPx4MSJE2jatCmqVOF3ok7Fz3lERESkl57PeQzjQnTo0CGkpKTY3QwiIiJyoYMHDyI5OdnuZpAMfs4jIiKiUGn5nMcwLkR169YF4N3I9erVs7k1RERE5AYVFRVISUnxfY4gZ+LnPCIiItJLz+c8hnEhEoYs1KtXjx/SiIiISBcOfXQ2fs4jIiKiUGn5nMfJSoiIiIiIiIiIiCzCMI6IiIiIiIiIiMgiDOOIiIiIiIiIiIgswjCOiIiIiIiIiIjIIgzjiIiIiIiIiIiILMIwjoiIiIiIiIiIyCIM44iIiIiIiIiIiCzCMI6IiIiIiIiIiMgiDOOIiIiIiIiIiIgswjCOiIiIiIiIiIjIIgzjiIiIiIiIiIiILFLV7gYQEVmpsKgM+4+eRIuE2khPrW93c4iIiIiIiCjKMIwjoqgx89PdeHHdj76fx/VuiclZaTa2iIiIiIiIiKINh6kSUVQoLCoLCOIA4MV1P6KwqMymFhERUdQqLgC2v+P9LxEREUUdVsYRUVTYf/Sk7O0crkpERJbJnwp8lXv+554TgP7T7WoNERER2YCVcUQUFVok1NZ1OxERkeGKCwKDOMD7MyvkiIiIogrDOCKKCump9TGud8uA2/7auyWr4oiIyDrH9um7nYiIiCISh6kSUdSYnJWGge2TuJoqERHZo2FrfbcTERFRRGJlHBFFlfTU+hjaJZlBHBERWS85wztHnL+eE723ExERUdRgZRwRERERkVX6TwfSBnuHpjZszSCOiIgoCjGMIyIiIiKyUnIGQzgiIqIoxmGqREREREREREREFmEYR0REREREREREZBGGcURERERERERERBZhGEdERERERERERGQRhnFEREREREREREQWYRhHRERERERERERkEYZxREREREREREREFmEYR0REREREREREZBGGcURERERERERERBZhGEdERERERERERGSRqA3jTpw4gUsvvRSdO3dGx44d8fLLL9vdJCIiIiIiIiIiinBV7W6AXWrVqoV169ahVq1a+P3339GhQwcMHToUDRs2tLtpREREREREREQUoaK2Mi42Nha1atUCAPz55584e/YsPB6Pza0iIiIiIiIiIqJI5tow7osvvsDgwYPRtGlTxMTE4MMPPwy6T15eHlq0aIEaNWqga9euWL9+fcDvf/31V3Tq1AnJycl46KGHkJCQYFHriYiIiIiIiIgoGrk2jDt58iQ6deqEefPmSf5+8eLFmDBhAh5++GEUFhaiV69eyMrKQlFRke8+F1xwAbZv3479+/fjrbfewi+//GJV84mIiIiIiIiIKAq5NozLysrCE088gaFDh0r+fs6cObjzzjsxZswYpKWlITc3FykpKZg/f37QfRMTE3HJJZfgiy++kH29yspKVFRUBPwjIiIiotCUlZVh1KhRiI+PR3x8PEaNGoVff/1V8TEejwfTpk1D06ZNUbNmTfTp0we7du0KuM/dd9+NVq1aoWbNmmjUqBGuu+46fP/99ya+EyIiIiJ9XBvGKTl16hS2bNmCAQMGBNw+YMAAbNiwAQDwyy+/+AK1iooKfPHFF2jbtq3sc86YMcP3YTE+Ph4pKSnmvQEiIiKiCHfTTTdh27ZtWLFiBVasWIFt27Zh1KhRio+ZPXs25syZg3nz5mHz5s1ISkpC//79ceLECd99unbtitdeew27d+/GypUr4fF4MGDAAJw9e9bst0RERESkSUSupnr06FGcPXsWiYmJAbcnJiaitLQUAFBcXIw777wTHo8HHo8H9957Ly655BLZ55wyZQpycnJ8P1dUVDCQIyIiIgrB7t27sWLFCnz99dfo3r07AODll19GZmYm9uzZI/kFqcfjQW5uLh5++GHfyIhFixYhMTERb731Fu6++24AwF133eV7TPPmzfHEE0+gU6dO+Omnn9CqVSsL3h0RERGRsogM4wQxMTEBP3s8Ht9tXbt2xbZt2zQ/V1xcHOLi4oxsHhEREVFU2rhxI+Lj431BHABcdtlliI+Px4YNGyTDuP3796O0tDRg5ENcXBx69+6NDRs2+MI4fydPnsRrr72GFi1aKH6JWllZicrKSt/PnI6EiIiIzBSRw1QTEhIQGxvrq4ITHD58OKhajoiIiIisVVpaisaNGwfd3rhx46DPb/6PAaA48kGQl5eHOnXqoE6dOlixYgXy8/NRvXp12fZwOhIiIiKyUkSGcdWrV0fXrl2Rn58fcHt+fj569OhhU6uIiIiIItu0adMQExOj+K+goABA8AgGIHAUgxylkQ+Cm2++GYWFhVi3bh3atGmDG2+8EX/++afsc06ZMgXl5eW+fwcPHtT6lomIiIh0c+0w1d9++w379u3z/bx//35s27YNDRo0QGpqKnJycjBq1ChkZGQgMzMTCxYsQFFREcaNG2djq4mIiIgi17333ouRI0cq3qd58+b49ttv8csvvwT97siRI7KjGJKSkgB4K+SaNGniu11q5INQ4damTRtcdtllqF+/PpYuXYq//OUvks/N6UiIiIjISq4N4woKCtC3b1/fz8LiCrfddhsWLlyIESNG4NixY3jsscdQUlKCDh06YPny5WjWrJldTSYiIiKKaAkJCUhISFC9X2ZmJsrLy7Fp0yZ069YNAPDNN9+gvLxcdhRDixYtkJSUhPz8fKSnpwMATp06hXXr1mHWrFmKr+fxeALmhCMiIiKyU4zH4/HY3Qg3qqioQHx8PMrLy1GvXj27m0NEREQuwM8P52VlZeHQoUN46aWXAHhXQW3WrBmWLVvmu0+7du0wY8YMZGdnAwBmzZqFGTNm4LXXXkObNm3w1FNPYe3atdizZw/q1q2LH3/8EYsXL8aAAQPQqFEj/Pzzz5g1axbWr1+P3bt3S85TJ4X7iYiIiPTS8/nBtZVxREREROReb775Ju6//37f6qhDhgzBvHnzAu6zZ88elJeX+35+6KGH8Mcff2D8+PEoKytD9+7d8dlnn6Fu3boAgBo1amD9+vXIzc1FWVkZEhMTccUVV2DDhg2agzgiIiIis7EyLkT8xpSIiIj04ucHd+B+IiIiIr30fH6IyNVUiYiIiIiIiIiInIhhHBERERERERERkUUYxhEREREREREREVmEYRwREREREREREZFFGMYRERERERERERFZhGEcERERERERERGRRRjGERERERERERERWYRhHBERERERERERkUUYxhEREREREREREVmEYRwREREREREREZFFGMYRERERERERERFZhGEcERERERERERGRRRjGERERERERERERWYRhHBERERERERERkUUYxhEREREREREREVmEYRwREREREREREZFFGMYRERERERERERFZhGEcERERERERERGRRRjGERERERERERERWaSq3Q0gIiJyu8KiMuw/ehItEmojPbW+3c0hIiIiIiIHYxhHREQUhpmf7saL6370/Tyud0tMzkqzsUVERERERORkHKZKREQUosKisoAgDgBeXPcjCovKbGoRERERERE5HcM4IiKiEO0/elLX7URERERERAzjiIiIQtQiobau24mIiIiIiBjGERERhSg9tT7G9W4ZcNtfe7fkIg5ERERERCSLCzgQERGFYXJWGga2T+JqqkREREREpAnDOCIiojClp9ZnCEdERERERJpwmCoREREREREREZFFGMYRERERERERERFZhGEcERERERERERGRRRjGERERERERERERWYRhHBERERERERERkUUYxhEREREREREREVmEYRwREREREREREZFFojaMO3jwIPr06YOLL74Yl1xyCd577z27m0RERERERERERBGuqt0NsEvVqlWRm5uLzp074/Dhw+jSpQuuvvpq1K5d2+6mERERERERERFRhIraMK5JkyZo0qQJAKBx48Zo0KABjh8/zjCOiIiIiIiIiIhM49phql988QUGDx6Mpk2bIiYmBh9++GHQffLy8tCiRQvUqFEDXbt2xfr16yWfq6CgAOfOnUNKSorJrSYiIiIiIiIiomjm2jDu5MmT6NSpE+bNmyf5+8WLF2PChAl4+OGHUVhYiF69eiErKwtFRUUB9zt27BhuvfVWLFiwwIpmExERERERERFRFIvxeDweuxsRrpiYGCxduhTXX3+977bu3bujS5cumD9/vu+2tLQ0XH/99ZgxYwYAoLKyEv3798fYsWMxatQoxdeorKxEZWWl7+eKigqkpKSgvLwc9erVM/YNERERUUSqqKhAfHw8Pz84HPcTERER6aXn84NrK+OUnDp1Clu2bMGAAQMCbh8wYAA2bNgAAPB4PBg9ejT69eunGsQBwIwZMxAfH+/7xyGtRERERERERESkV0SGcUePHsXZs2eRmJgYcHtiYiJKS0sBAF999RUWL16MDz/8EJ07d0bnzp2xY8cO2eecMmUKysvLff8OHjxo6nsgIiIiIiIiIqLIE9GrqcbExAT87PF4fLddfvnlOHfunObniouLQ1xcnKHtIyIiIiIiIiKi6BKRlXEJCQmIjY31VcEJDh8+HFQtR0REREREREREZJWIDOOqV6+Orl27Ij8/P+D2/Px89OjRw6ZWERERERERERFRtHPtMNXffvsN+/bt8/28f/9+bNu2DQ0aNEBqaipycnIwatQoZGRkIDMzEwsWLEBRURHGjRtnY6uJiIiIiIiIiCiauTaMKygoQN++fX0/5+TkAABuu+02LFy4ECNGjMCxY8fw2GOPoaSkBB06dMDy5cvRrFkzu5pMRERERERERERRLsbj8XjsboQbVVRUID4+HuXl5ahXr57dzSEiIiIX4OcHd+B+IiIiIr30fH6IyDnjiIiIiIiIiIiInIhhHBERERERERERkUVcO2ccERGR2xQWlWH/0ZNokVAb6an17W4OERERERHZgJVxREREFpj56W5k521AzrvbkZ23ATM/3W13k4hsVVZWhlGjRiE+Ph7x8fEYNWoUfv31V8XHeDweTJs2DU2bNkXNmjXRp08f7Nq1y/f748eP47777kPbtm1Rq1YtpKam4v7770d5ebnJ74aIiIhIO4ZxREREJissKsOL634MuO3FdT+isKjMphYR2e+mm27Ctm3bsGLFCqxYsQLbtm3DqFGjFB8ze/ZszJkzB/PmzcPmzZuRlJSE/v3748SJEwCAQ4cO4dChQ/jXv/6FHTt2YOHChVixYgXuvPNOK94SERERkSYcpkpERGSy/UdPyt7O4aoUjXbv3o0VK1bg66+/Rvfu3QEAL7/8MjIzM7Fnzx60bds26DEejwe5ubl4+OGHMXToUADAokWLkJiYiLfeegt33303OnTogA8++MD3mFatWuHJJ5/ELbfcgjNnzqBqVX70JSIiIvuxMo6IKIoUFpVhydZiR1dkuaGNerVIqK3rdqJIt3HjRsTHx/uCOAC47LLLEB8fjw0bNkg+Zv/+/SgtLcWAAQN8t8XFxaF3796yjwGA8vJy1KtXj0EcEREROQY/lRARRYmZn+4OGCo5rndLTM5Ks7FFwdzQxlCkp9bHuN4tA97bX3u3ZFUcRa3S0lI0btw46PbGjRujtLRU9jEAkJiYGHB7YmIiDhw4IPmYY8eO4fHHH8fdd9+t2J7KykpUVlb6fq6oqFC8PxEREVE4WBlHRBQF3DBnmRvaGI7JWWlYOr4H5tzYCUvH98CkCAgZicSmTZuGmJgYxX8FBQUAgJiYmKDHezweydv9iX8v95iKigpcc801uPjiizF16lTF55wxY4ZvIYn4+HikpKSovVUiIiKikLEyjogoCrhhzjI3tDFc6an1I+a9EEm59957MXLkSMX7NG/eHN9++y1++eWXoN8dOXIkqPJNkJSUBMBbIdekSRPf7YcPHw56zIkTJzBo0CDUqVMHS5cuRbVq1RTbNGXKFOTk5Ph+rqioYCBHREREpmEYR0QUBdwwZ5kb2khEyhISEpCQkKB6v8zMTJSXl2PTpk3o1q0bAOCbb75BeXk5evToIfmYFi1aICkpCfn5+UhPTwcAnDp1CuvWrcOsWbN896uoqMDAgQMRFxeHjz/+GDVq1FBtT1xcHOLi4rS8RSIiIqKwcZgqEVEUEOYs8+e0Ocvc0EYiMkZaWhoGDRqEsWPH4uuvv8bXX3+NsWPH4tprrw1YSbVdu3ZYunQpAO/w1AkTJuCpp57C0qVLsXPnTowePRq1atXCTTfdBMBbETdgwACcPHkSr7zyCioqKlBaWorS0lKcPXvWlvdKREREJMbKOKIIUFhUhv1HT6JFQm0GFyRrclYaBrZPcvSx4oY2EpEx3nzzTdx///2+1VGHDBmCefPmBdxnz549KC8v9/380EMP4Y8//sD48eNRVlaG7t2747PPPkPdunUBAFu2bME333wDAGjdunXAc+3fvx/Nmzc38R0RERERaRPj8Xg8djfCjSoqKhAfH4/y8nLUq1fP7uZQFIvU1SeJiCIRPz+4A/cTERER6aXn8wOHqRK5WKSvPklEREREREQUaRjGEbmY0uqTREREREREROQ8DOOIXIyrTxIRERERERG5C8M4Ihfj6pNERERERERE7sLVVIlcjqtPEhEREREREbkHwziyVWFRGUMkA6Sn1uf2IyIiIiIiInIBhnFkm5mf7g5YCXRc75aYnJVmY4uIiIiIiIiIiMzFOePIFoVFZQFBHAC8uO5HFBaV2dQiIiIiIiIiIiLzMYwjW+w/elLX7UREREREREREkYDDVClk4cz31iKhtq7bQ8U56YiIiIiIiIjISRjGUUjCne8tPbU+xvVuGfAcf+3d0tDAjHPSEREREREREZHTMIwj3eTmexvYPklXmDY5Kw0D2yeZUrlmVBuJiIiIiIiIiIzEOeNINyPne0tPrY+hXZIND8g4Jx0RERERERERORHDONLNqvnewuGGNhIRERERERFR9GEYF0UKi8qwZGsxCovKwnoeYb43f0bP9xYuN7SRyK2MupYQERERERFFI84ZFyWMXszAzPnejOKGNroJV6YlgAujEBERERERhYthXBQwazGD9NT6jg9l3NBGN2AAQwAXRiEiIiIiIjICh6lGAS5mQOGQC2AWby6yqUVkF15LiIiIiIiIwscwLgpwMQMKh1zQMumDHZj56W6LW0N24rWEiIiIiIgofAzjogAXM6BwKAUtL677kZP4RxFeS4iIiIiIiMLHOeOiBBczoFAJAYx4qKpg/9GTPJ6iCK8lRERERERE4WEYF0W4mAGFanJWGlok1MakD3YE/Y5DFKMPryXW4SrGRERERESRJ6qHqWZnZ6N+/foYPny43U0hcrwRl6ZyiCKZqrCoDEu2FnPo8//M/HQ3svM2IOfd7cjO28A5GomIiIiIIkRUV8bdf//9uOOOO7Bo0SK7m0LkChyiSGaZ+enugKHQ43q3xOSsNBtbZC+5VYwHtk/ieUdERERE5HJRXRnXt29f1K1b1+5mENkmlEqk9NT6GNolmYEAGUYueIrmCjm5VYzlbo8krJAkIiIiokjn2jDuiy++wODBg9G0aVPExMTgww8/DLpPXl4eWrRogRo1aqBr165Yv3699Q0lcigOgSOnsDt4ckL4I26D3FyMkT5HI69LRERERBQNXBvGnTx5Ep06dcK8efMkf7948WJMmDABDz/8MAoLC9GrVy9kZWWhqKjI4pYSOQ8rkchJ7AyenBD+SLVBWMXYX6TP0cjrEhERERFFC9fOGZeVlYWsrCzZ38+ZMwd33nknxowZAwDIzc3FypUrMX/+fMyYMUP361VWVqKystL3c0VFhf5GEzmEUiVSJHf2yZmE4Mk/iLEieHLCvGxKbYi2ORp5XSIiIiKiaOHaME7JqVOnsGXLFkyePDng9gEDBmDDhg0hPeeMGTMwffp0I5pHZLtoHQJHzmVH8OSE8EetDcK/aMDrEhERERFFC9cOU1Vy9OhRnD17FomJiQG3JyYmorS01PfzwIEDccMNN2D58uVITk7G5s2bZZ9zypQpKC8v9/07ePCgae2n0Dhh3ie3iMYhcOR8Vi8O4oTwxwltcApel4iIiIgoWkRkZZwgJiYm4GePxxNw28qVKzU/V1xcHOLi4gxrm1sUFpW5YojUzE93Bwz1Gte7JSZnpdnYIueLtiFwTuGWcypSKG1vu4bHOq0NTsLrEhERERFFg4gM4xISEhAbGxtQBQcAhw8fDqqWI3luCbicMO+TW0XTEDgncMs5FSm0bG8nhD9OaIOT8LpERERERJEuIoepVq9eHV27dkV+fn7A7fn5+ejRo4dNrXIXN61qpzTnEpFTuOmcigR6trdVw2OVhtJbPUSXiIiIiIjs49rKuN9++w379u3z/bx//35s27YNDRo0QGpqKnJycjBq1ChkZGQgMzMTCxYsQFFREcaNG2djq93DCROba8U5l8gN3HRORQKnbW+nV0Vy+DSRjYoLgGP7gIatgeQMu1tDREREFnBtGFdQUIC+ffv6fs7JyQEA3HbbbVi4cCFGjBiBY8eO4bHHHkNJSQk6dOiA5cuXo1mzZnY12VXcFHBxziVyAzedU5HASdvb6UPpnR4UEkW0/KnAV7nnf+45Aeg/3a7WEBERkUVcG8b16dMHHo9H8T7jx4/H+PHjLWpRZHFbwMU5l8jp3HZOuZ2TtrfTqvT8OT0oJIpoxQWBQRzg/TltMCvkiIiIIpxrwzgyn9sCLq2TfnM4FplF7dhy2znldk7Z3k6q0hNzclBIFPGO7ZO/nWEcERFRRGMYR7IiMbTicCwyi9ZjiytFWssJ29tJVXpiTg4KiSJew9b6biciIqKIwTDOwewMwyIxtOJwLDILjy1S45QqPTEnB4VEES85wztHXMCccRNZFUdERBQFGMY5lJ1hWKQGCxyORWbhsUVaOKFKT4pTg0I1kVi9TVGo/3TvHHFcTZWIiCiqMIxzILvDsEgNFjgci8zCY4vczqlBoZxIrN6mKJacwRCOiIgoylSxuwEUTCkMs0KkBgvCcCx/HI7lboVFZViytRiFRWW2tmH/0ZPITm8acDuPLSJzyH1hZed1gIiIiIhID1bGOZDdYVgkzyHk1uFYFMwJlTHiNmSnN0WvNo14bBGZKFKrt4mIiIgoejCMcyAnhGFaQyu3zdnjtva6hdXb1e6h3HJtWFp4CLdmNuexRWQiu7+wIiIiIiIKF8M4h3JCBZfaHEJOqEzSw23tdQs7tqsTKmOc0AaiaOSEL6yIiIiIiMLBMM7BnDyhthMqk/RwW3vdwq7t6oTKGCe0gShaGfWFFauliYiIiMgOXMCBQmL3IhN6ua29bmHXdnXCYhxOaANRNEtPrY+hXZJDPudmfrob2XkbkPPudmTnbcDMT3cb3EIiIiIiImmsjKOQuK0qyG3tdQs7t6sThnI7oQ1EpB+rpYmIiIjITqyMo5C4rSrIbe11C7u3a7iVMZHSBrJOYVEZlmwtRmFRmSn3J2uwWpqIiIiI7MTKOAqZW6qChDmBBrZPckV73cYtxwGRFD1zhuldrISLxoTPrDndWC1NRERERHZiGEch8e8gDe2SbHdzZLEzrE24HV4nLzbiVpxY3nx6rg96hzVGyjBIO49DM6/fXJGViIiIiOzEMI50c0vAFSmdYbNJ7U9WuoUn3ADDLeeYm+m9PigNazTi/qEyMyyz8zi04vrNql4iIiIisgvnjCNd5DpITpwPiXMCqZPbn1xhMHThrtBo1DnGucqU6b0+6B3WaMUwSDNXA7XrWi8ct2v3HJb8vZbrt55jn3M+2qusrAyjRo1CfHw84uPjMWrUKPz666+Kj/F4PJg2bRqaNm2KmjVrok+fPti1a1fAfRYsWIA+ffqgXr16iImJUX1OIiIiIqsxjCNdtHRgnRICmN0Zdsr7DIeWjq1Tw1YnEB8DRgQYRoTIZoY0kULv9UHvYiVmL24id6wt3lxkyHXJji8z/I/b51btk7yP2vV74uJCHvsuctNNN2Hbtm1YsWIFVqxYgW3btmHUqFGKj5k9ezbmzJmDefPmYfPmzUhKSkL//v1x4sQJ331+//13DBo0CP/4xz/MfgtEREREIeEwVdJFrQPrpOF1Zs4J5KT3GQ6twaTRQ+vkuGmeNKlj4KLEupL31bP9wg2Ro314ttZjKJTrg95hjWYOg5QLxSZ9sMP3/+Fcl6xe4EDquBVT2z8TFxdiaeGhgNui6dh3m927d2PFihX4+uuv0b17dwDAyy+/jMzMTOzZswdt27YNeozH40Fubi4efvhhDB06FACwaNEiJCYm4q233sLdd98NAJgwYQIAYO3atZa8FyIiIiK9GMaRLkodWCeGAGZ0hp34PkMltT+liDvgZoRmVgScRrVb7hiYNayj5P31BBjhhshWzVXmFP77dOWuUl3HkNT1Qe0Y0btYidGLmwjtO332nOp9w7kuWb3Agdxx+8CVrdGsYW3Vc7awqCwoiPN/7kg89t1u48aNiI+P9wVxAHDZZZchPj4eGzZskAzj9u/fj9LSUgwYMMB3W1xcHHr37o0NGzb4wrhQVFZWorKy0vdzRUVFyM9FREREpIZhHOk2sH0S4qp6Rzj3advY18lxaghgdGfYSe/TiHBJHEiIAw1xB9yM0MyKgNPIdssdA9ViqxgSYIQTIltd0WQn8T4V03IM+V8fnF7xKm5f55R4bDtYrviYcK5LVi5wIHd8+v+NkVNYVIb3Cg7qfm6yV2lpKRo3bhx0e+PGjVFaWir7GABITEwMuD0xMREHDhwIqz0zZszA9OnTw3oOIiIiIq0YxpEu4s5g5Zlzvo6S1hDATUMRpTgl7DAyOPAPJNJT68t2wM0IzZQ60kYFnEa3W+kYGNol2ZAAI9QQ2eqKJrtoGdYIaD+GnF7xKtW+bQfLMWtYR1SLrYLTZ88FDFEVhHtdEh+HZl2/Qz1u1QLZoelNJZ/D7X+HnGzatGmqodbmzZsBADExMUG/83g8krf7E/9ey2PUTJkyBTk5Ob6fKyoqkJKSEtZzEhEREclhGEeaqXVWtXSmnF55ooWRYUeoHUKzgwO5IMjoqkC1jrRRAafR7VY7BoyuxtQrnIqmwqIy30qWWqqS7KJ1IQE98yLK3e6EbaBUjTm0S7LvPmaGsGZfv/Uet2qB7ND0ppgzIj3o9kj4O+Rk9957L0aOHKl4n+bNm+Pbb7/FL7/8EvS7I0eOBFW+CZKSkgB4K+SaNGniu/3w4cOyj9EqLi4OcXFxYT2HIxQXAMf2AQ1bA8kZdreGiIiIZDCMI820dFaVOlNOrzzRw4jhW+F0CI0MDvQEgkZWBap1pPu1a6T7OeWYUc1o5RC+UIQSCIqPyedW7UN2elP0atPIce9Ry77TE0Y5peJVjpb2mXlMWnX91nPcyl0Hb+qWghsyUmQr4iLl75BTJSQkICEhQfV+mZmZKC8vx6ZNm9CtWzcAwDfffIPy8nL06NFD8jEtWrRAUlIS8vPzkZ7uDVpPnTqFdevWYdasWca9CbfKnwp8lXv+554TgP4cektEROREVexuALmH1s5qemp9DO2SHNSxUQqQ3EjufWoh1yEsLCrT9HijgoOZn+5Gdt4G5Ly7Hdl5GzDz092K9xcqwvyFWn0jt9/Tkrwrkq7+/oimNmlhZLvFzxvqMeA0cuHo0sJDqsdHYVEZlmwt1nz8GkFuny4d3wNzbuyEpeN7YJLOaqe+bQMDYCcN79V6DJt1TDrx+i13vZML4gBnvo9olZaWhkGDBmHs2LH4+uuv8fXXX2Ps2LG49tprAxZvaNeuHZYuXQrAOzx1woQJeOqpp7B06VLs3LkTo0ePRq1atXDTTTf5HlNaWopt27Zh3759AIAdO3Zg27ZtOH78uLVv0krFBYFBHOD9ubjAjtYQERGRClbGRSCnzekjcHrliZXCrWwzYqhsqBUiRlXfyO333aUndLdJC6dXstlNSxghtS/sHPKntE+F96NlP4vfQ792jXBfvzaOO0bsPIadeP0O5TroxPcRzd58803cf//9vtVRhwwZgnnz5gXcZ8+ePSgvP79QyUMPPYQ//vgD48ePR1lZGbp3747PPvsMdevW9d3nxRdfDJi37oorrgAAvPbaaxg9erSJ78hGx/bJ387hqkRERI4T4/F4PHY3wo0qKioQHx+P8vJy1KtXz+7m+FjRMQ4n7BO376+9W+quXokEhUVlyM7bEHT70vE9dAdqoe6LJVuLkfPu9qDb59zYyTcHldmkQpDV3x+xtU2hcvuE8HLHpJj/vpB7zANXtrZtvjm910CjzsVo4NTrt95zz+734dTPDxTIdfupuAD495XBt49ZxTCOiIjIIno+P7AyLoKYNReOuKMTzuT0rE7yMmoRiHD2hRMqRMTHAwDJME5vm6wOxiJhQnipY1KK/76Qq6Z7btU+PLdqn+XbIZRroNMXbnASp16/9V4Hnfo+iMKSnOGdIy5gzriJDOKIiIgcimFcBDGjU2lGyGD3SpNOYXeH0MhVYcNth/9rhtsmq4OxSJoQXjgmhdVUi47/jqWFh3y/F+8LtZDU6u0QyjXQCaG0mxh5/bazmpR/hygi9Z8OpA3maqpEREQuwDAugpw+e07y9lA7lZEUMjiV3R1CuwNBo9tkxzEbaZVV4mPy1szmsvtCSzWdldshlGDNKaF0tImEalIiR0rOYAhHRETkAgzjIoS4YyMIp1MZaSEDBfKvSgl1PjYzFwsxcoVWM45Z4b0bHYI7jdq+8K+me25V8ATiVm6HUIM1J4bSkYxf9BARERFRtGMYFwGkOjYAMGtYR4y4NDXk53Xj8C23T6JvFSOqUpxY2WLVMSt+751T4rHt4PnV/qKtskoI7CrPnLO9wizUYE0udOQ1xXj8ooeIiIiIoh3DuAgg17GpFlslrOd12/AtpXCIHerzjKhKcWplixXHrNR733awHLOGdUS12CquPMaMOj+cUmFm1PBvJwbOkcCNX/QQERERERmJYZyLWTFMzimdazVK4dDKXaXsUPsxoirFyZUtZh+zSuF3qMN97WR04GT3PIhGcWrgHAnc9kUPkaMVF3DBBiIiIhdiGOdSVg6Tc0PnWi4gWbvnMDvUIkZUpTi9ssXMY9bp710PBk7ynBw4G8XOimG3fNFD5Gj5U4Gvcs//3HOCd0VVIiIicjyGcS4UicPkwiUXhJSW/yl5eyR1qPXSU5Ui11mP5sqWSHrv0RA4hSqSQlcpThiC64Yveogcq7ggMIgDvD+nDWaFHBERkQswjHOhSBsmZwSpgAQAFhcUS94/UjrUodJSlaLWWY/EyhatlUKR8t4jPXAKRySFrmKsiCSKAMeCV6/23c4wjoiIyPEYxrkQO9DSJmeloUVCbUz6YIfi/SKlQx0upaoUrZ31SKps0VspZNV7VwsIwxlqGMmBkxEiIXT1n1tUqJxmRSRRBGjYWt/tRERE5CgM41yIHWh5civIPnBlazRrWNu1HWqrGd1Zd/pqtk6tFFILCI0YahgJgZOZzAxdzT4vxMeHIDu9qeT9o/0LHSJXSc7wzhEXMGfcRFbFERERuQTDOJdiB1qaXGeyT9vG3EY6GFl96YS5qdQ4sVJILSA0MkA0u8rP6WGsHcw+L6SOD8HSwkPITm+KpYWHfLfxCx0iF+o/3TtHHFdTJSIich2GcS4WSUMEjWJ31WCkhA5GbUenVpyJOXHot1pA6MQAUYobwlirWXFeyB0fgl5tGuHWzOaS1ysrrmN6XiNSrqtEpkjOUA7higsY1hERETkQwziKOHZVDUZa6GDEdnRLYGR3iCtFLSDUGyDaEWi4JYy1mhXnhVqQLBwH4tez4jqm5TWE43X93iMBFXxuv64SWSp/qmgY6wRvNR0RERHZjmEcAYi8ygOrqwYjNXQIdzs6seJMjtOGfqsFhHoCRLuCYreEsVaz4ryQW2EakD9OtAyNDvf80HKtlJvrTuq+RCSjuCAwiAO8P6cNZoUcERGRAzCMo4ir6LJDtIQOejvjTqw4k+L/voZ2Sba7OT5qAaGWANHOoFhr6BRpXwaoseq88D8+/FdTlXsdpevYyl2lhvydULtWKs11J75vuKLtuKMoc2yf/O0M44iIiGzHMC7KRWpFl9XcVAEWqlBDW6dVnIlZEUaH0+lXq04Ufl9YVIYlW4uDXkNrUGxGMKEldIrWLwOsOi/0VLfKXa9Onz1n2N8JtWul2lx3Ss+hR7QedxRFGrbWdzsRERFZimFclIuWii6zuaUCTKA3eAk3tHXqYiNmhNHibWtEp19tfym9hpag2MxgQil0ivYvA5x2Xshdx6rFVpG8fyh/J6Reo1+7Rr7/VwvajLiuRvtxR1EiOcM7R1zAnHETWRVHRETkEAzjolw0VHRZobCoDBcl1sWsYR1Vh4LZLZTgJVJDW6Pfl3jbZqc3DZh8HtDf6VfbX2rBglpQbEUwIRc6Repx5WZS4WlhUZnkfUP9OyG8xtxVe7FmzxGs/t77Tzi2xcfr0PSmuLxNo7DnqhPeE487ihr9p3vniONqqkRERI7DMC7KmVXRFU1z8UiFJVbMOxbKNg41eInU0NbI9yW1bcVBnEBrp1/L/tISLChVp9kZTKzfe0TydrcfV24nDk/N+juxZk/g/heObaOH8EqF5FJ43FFESs5gCEdERORADOOinBkVXdE0F49dw51C3cahBi9uG4arlZHvS8tcVwKtnX4t+0troChXnWZX0FpYVCYZVg5Nb+r640osEr6cMDogUzu2jRrCKxeSi6tWI+F6RkRERETuEbVh3CeffIIHH3wQ586dw6RJkzBmzBi7m2QZoWO4fu+RgM6IERVd0TYXjx1VReFs43CCF6cvxBAqo96X3DYMp9OvZX+FGyjaFbTKnTuXt2kkebtbRdKXE0bOcWdVCCx3nPVq0wi3ZjaPuOsZEREREblDVIZxZ86cQU5ODtasWYN69eqhS5cuGDp0KBo0aGB300wn7hj6MyI0szqcsrvixI6qonC2sRHBTSR2Wo14X3LbdlJWWsidfq37yz9QPH32HKrFVkFhUZnm17IjaI3Uoc/+nPjlhN3XTIFVIbDScRap1zMiMlFxAefgIyIiQ0RlGLdp0ya0b98eF154IQDg6quvxsqVK/GXv/zF5paZS6pjKBZuaGZlB9sJFSd2VBWFu40jtcLNCeS2bTidfq37Kz21PlbuKg35nLA6mIjUoc/+nLJQgFI1tJ1VelZci6LhOKMoZXQoxJBJXf5U0eq0E7yLZBAREYXAlWHcF198gaeffhpbtmxBSUkJli5diuuvvz7gPnl5eXj66adRUlKC9u3bIzc3F7169QIAHDp0yBfEAUBycjJ+/vlnK9+CLbTMaRVuaGZUx0etesNJFSdWh1tGbGNWhJhHy7bVW50k9Zzi5zDznDCrmirSg2EnVP+ZXQ0dLiuuRZF+nFEUMjoUYsikrrggcBsB3p/TBjO8JCKikLgyjDt58iQ6deqE22+/HcOGDQv6/eLFizFhwgTk5eWhZ8+eeOmll5CVlYXvvvsOqamp8Hg8QY+JiYmxoum2UusAqgU6Wjvk4XZ8tFS8OaXiRGB1uMXOpXsZUdEp9RwXJdaVvG+454TZFaiRHAzbXZVlRTW0nrbYeb2K5OOMoozRoVAozxeNVXTH9snfbtc2cMt+cEs7iYgs5sowLisrC1lZWbK/nzNnDu68807fogy5ublYuXIl5s+fjxkzZuDCCy8MqIQrLi5G9+7dFV+zsrISlZWVvp8rKirCfBfWk+oYDk1visvbNFLtIOntkIfa8dFa3eOEihO7sXPpPkZUr8k9x6xhHSXvH8454aQKVLeyMzi3ohpaCydMKSCwOxQkCpvRoZCe5ysuANbNBvauPH9btFTRNWyt73azuaWa0S3tJCKyQRW7G2C0U6dOYcuWLRgwYEDA7QMGDMCGDRsAAN26dcPOnTvx888/48SJE1i+fDkGDhyo+LwzZsxAfHy8719KSopp78FMk7PSsHR8D8y5sZP3vyPSMbRLsmpFnFSHvLCozPD2KVW8+UtPrY/s9KYBt3EeIHI6rcd3KM9RLbYKxvVuGXBbuOeEEe01WmFRGZZsLTbl+mOW9NT6qtdZM4RbDW0EK/9+qJn56W5k521AzrvbkZ23ATM/3W15G4jCZnQopPX58qcC/74yMIgDvEFLcUFor+0myRneIMlfz4n2VHrJVTM6bT+4pZ1ERDZxZWWckqNHj+Ls2bNITEwMuD0xMRGlpaUAgKpVq+KZZ55B3759ce7cOTz00ENo2LCh4vNOmTIFOTk5vp8rKipcG8jpraiyckio1oq3mZ/uDpiIPDu9KSbprLRwcoWEk9vmRG7ZXkZUdCo9x9AuyYZWYTmtAtVJFVZuEE41tFGcMqUAqzwpYgihUEC1kSgU0jMsUOvziUMVf3YO1bRS/+ne4bt2D7l04pBZKW5pJxGRTSIujBOI54DzeDwBtw0ZMgRDhgzR/HxxcXGIi4szrH1WCyessLJDrmWOJalO1dLCQ7g1s7nm9+bkTr2T2+ZETt1eUuecUYtvSAUsRqzcquW17KpAZZgSGquHyYqPe6cEuk4JBYkMoRQKhTIsUC1kkgtVBHYN1bRDcob9QZJR1ZFmz+XmtKG9REQOE3FhXEJCAmJjY31VcILDhw8HVctFOqFTtH7vkYAqMr1hhdUdcrXOo9rQObVOp9Wdev/OqVr7GDjoo2d7WVk9pxQQGhGOTM5Kwy8Vf/rO6yWFh9C4Xg1TQkirwhy1/SN33s9dtRev3d7NlDa5mXh7WnH9kDvunRDoOiUUJDKMVCgUzuIOSiHT2dPyj7NrqKaTmR1yaalmVGPFXG5GtJNCw0UziFwh4sK46tWro2vXrsjPz0d2drbv9vz8fFx33XU2tsxa4k6Rv1DCHaurK5Q6j3Kdp/V7jyDn3e2+n+VCRysrJJT2Q6irxLplSKYcI9uvtr2MCqT10BIQhhuOFBaVBbwfqdcwktlhjpbqRrnzfs2eIygsKnPluWAWO6pFlY57tb8fVlzTnFTlSWQaM4YFikMbQZuBQO+H2NEXs2rBgnCGzBq9Iq8Ss4b2MmySp/UY5DYksp0rw7jffvsN+/ad/8Cxf/9+bNu2DQ0aNEBqaipycnIwatQoZGRkIDMzEwsWLEBRURHGjRtnY6utI9UpEgsleHLK6p1yw/SWaAwnrKqQUNsPoawS69QhmVrJtT/Uzrjc9jpw7CQmLi4MCqwEZgZXVoS9kTTkTmt148pdpeKH+rjxfZvFrupatWNS7u+Hldc0O1e2JTKV0KmWq2DzHxaopwOuNFccg7hgVoZcQOhDZq2Yy018nBn5/sVhk1uCYSvCL63HIFe5JXIEV4ZxBQUF6Nu3r+9nYWGF2267DQsXLsSIESNw7NgxPPbYYygpKUGHDh2wfPlyNGvWzK4mW0rLSodOHJqjJ5ARd6r2Hz0ZFMYB0p10qyoktOwHcfuU2ub2Iaxy7fcfbgno64xLbS8AeG6Vyvw2MC/AsSLsjYQhd8L5fuCYtmpQpWDbTe/bLHq2pxlCOSatuKZJDdd1w/WSSDNxp/rCrsDPW87/7D8scMldwLeL/X43QbkDrjRXnNMn4bej6sctCxaYPZebnsqsvfne/2/TX9s2kgqb9q70/nNyoGRV+KXlGLQ6NCYiWa4M4/r06QOPx6N4n/Hjx2P8+PEWtchZ1DqmThyao1QdIRfSaelUHTh2UnIImxUVEloCAqn7yLXNrdVQaiFBuMMthe21ds9hTSGcwKwAx4qw1+1D7pSGbwv8949SsO2m920WvdvTjGGheo5Jq4JDt1cSE/nIBUtSneqftwBD5gGx1QLvLw7igPMdcED6+ZXCGTMn4Q83SNMTfBgZ2rllwQIz53ILtTJr3UxtAZVSQOzUQMnK8EvLMeiW0NiJOLSXDObKMI6UyQ3jvLxNI0cOzVGqjli5q1RTZ0qpQuq5VfskH2d2hYRcmwT+HVUt1RtGVUOZNT+T8Lynz55DtdgqaJFQO2j/aaW3M56eWl9TJaJALcAJdxtZEfa6dcidlmH04v0jd4zPGtYRIy5NNbR9obBzHke929PMgErLMak3OAyV2yuJiXyUgiW5TnVsNaDTyPM/FxcEB3GCZQ8Av+yUfn6p0AbwDgs0S7gVRHqCD7nXkupwa+mEu2nBglDmctOyDUKtzAK0BVRqwaYTAyUrwy8tx6BbQmOnkbpemDEfIkUVhnERyk0ddbkQZe2ew7o6U0oVUnZ1wsT7AQheTVVr59iIaiizOuJaOthSpOb6A0LrjKs9RmsgbdQ2smI4nBuH3Mmd7w9c2RrNGtaW3D9yx75dQZx/+Kb1CwMtzxXKvtSzPdUCKiNCRaVjMpQgNlRurSQmCqAWLMl1nn9YHRjGKVUT+Qdx4ucHzoc2e/OBH9cAB78xb1igERVEcu913Wzg5nfVX+tESfBQXuF3/rfJvW+zFiwwg5653LSGpEpBjxDmHd8v/zpqAZVcQKz2+nZSC7+MrrZSOwaltuElI8+fO04+Zu0id73gvHsUJoZxDhZux8gtHXW9wYtSZ0qpQiqcTlg4+0K8H/z/X2/1Rjghq1mVIlo62P7EIUHjejUMGW5pREWolm3k9tVs7SZ3vvdp21hxezrlCwa14PnFdT+iRUJtTUGhEcGvnu2pdG0MN1TUIpQgNlSRMK8ikWpFTXIGcMmI4Kq3bxcD3e4636nWG1CIAxHh/9fNDLyfXFAWarhgRAWR3Hvdu9LbLuF55F5LaiivmJb37R+GGs3qoXJ6QlK5yqzdy+QDNH9ajlUhbHr/TuDXn87ffqHBC0UIwt3eStVqZi1GoRa0+gd2P6wGvn3H+w9gqCRF6QsNgdFDjzkkNiowjHMot851E0pQIVf10qdtY8k5wNQ6U0Z3wozeF/7bKJTgMNSQ1eiQUm3eJznikEBvyKJ0jIUb2KhtI7eel04SToWnUV8whBqoag2eJ32wA/uPnlQ8NowKx/VsT7lr4Omz5ywZ0hlqEBsKt8+rSARAW+Vbq37SQ1D9Ayy1aiItr6s1KAtnmKkRw+eSM7yBxt6Vwb/bmx96QCkW6vu2cj48o+gNScWVWQDw7yvVX0fvkF7/IA4Afi4IDFyNYMSw6WP7vNtDXK1m92IUwnZaenfg7U6de89OWq8X/teYcHC126jBMM6B7J7rJtSOajhBhVyIoqUzJTXfmlGdMLl90SKhtm9etHC2UXZ6U8n7mVG9YWRIGeqwVLn9oDVk0XKMhRPYKG0ju89Lp1K6Xsj9zqwqNy3XrnCuU3rmJVQ7NowMx7VuT7lrY7XYKoa1RYmVAVlhURkuSqyLWcM6hnStJnIELZVvWgMs/4Dk6F5g/b+kHycXiGh5nXCHmYYz55p/yNX7Iekwbt1M4FDh+cojqaF6QnWQmlDet5Xz4RkplJDUvzJru8w27T35/P9rXU1VYMU8bOFub7X97YTFKKJxMYdQAnGtX2ismwmc+TO84Mzpq92yYs9QDOMcyM65bkLtqCoFFUDwPGlSpEIUtU6mXHuN6uzL7YtJH+wIek01UttoaeEhZKc3DVhR1IjOqVQoYVRHWO+wVH8D/nc8hMKKMExpGy3ZWiz5mGieg0rpeiEVPPfyGzJs9DB6qbaIrwHhHkN6g+u5q/bitdu7Bd1eWFQmW1EaahCvdXtKXRsLi8oMbYve1zdCYVEZ1u45DAAoOv57wDV1XO+WGNol2ZDXIbKcWuWb1gBL6ED9sFr6+dSGx2l5HbmOvZ5qkVDmXJMKPeQ6zuLKI/Fr1U0Kfo/whPa+hXnqigu828Cs+fC0BiehdqLDXZhCLrTTE8CJ227FIgThbG8tgYoTFqPQuh3dHMD4t108XFpPIC6+XsgNvQ43OHNyQGpHxZ6bjz0NGMY5kF1z3YTTUZULreau2os1e474fg5lWJ9cJ1OtvUZ09rVs83C3Ua82jXBrZnPDOqdKAYkRHWG1eZ9Onz2H7Qd/xVubDko+1uhg1OgwTG4bmXleunEeOrUAXip4FgISo4f3yrVFfB5clFhX8vHiY0huf8iFtc0TagcE9II1e46gsKgs4DmUqkqtGkYpNY+llUM6jbg2Ky2iIaYncHXjuUgRTktnWS3AEnegxIbMA7qMUm+L2uvItVVvtYiehQXkQo8xq4CqNYLnufO/j9Bh9n8tufcYyvveuxJYcpf8SraAMfPhaQmgwu1Eh7MwhVqYp9bZFrf9khHA0AXmr1wrt13PnvZW+4W7qmw4i1GEuuKvmJagVW77K7VFa5vNpnbt0xuc+V8vkjPkrzHhBGdOXe3Wjoo9peuW3uPJoaEewzgHsmuum3DCDrlAwj+IA4ytZLIinElPrR9UuRbqayqFOUbOhaUWqIb7Wlrmfboosa5kGBdOcGVlSC21jcw6L906D53S+adGb9WsGqEiSu01Zw3rKPk7/2NIbX/IhbUrd5Vi9feB1zsg8NogV1X6wJWtTZk3TYk4dHLKAhlahDJMXss12q3nIkU4rVVJcgGWVAdKLLaavvYI811tf8cbTMRWO9/BkQsXzOq0KYUebfrLh3HCfaTaI7UtlQJCpXnqlII4QP98eKEEUEZ1opWOMbVOrn+YJxwzxQXqlUpSbRe26dAF+gJCvZ1xqe19YQbw8b3y7RXoHT6+bnbg8aO0X6UCCkB72CreDkpBq9r2lwrqWvULfh67Kqq0zJNZ+Ib3v6Fcm+SuMeEEZ0rnuZ2BktUVe0rXLb0Vjg6eg49hnEPZ0TEKJ+yQCir6tWuk2jkNh1HhjFIlxMxPdwcEcb0vSsC6/x4N6TWtCFmtCijV3ocZ79UJE7KHcl6qzanm1nnowj3/jKiaBfQFM9ViqygeQ1r3h1RYe1+/NpLXu/V7j/iGSMqdn80aWht+yYVORg8dNpJwHkktNqGF2nHp5nORokA4VUlaVgHU23GUqzYROjhmVIvIUQo9wqk80kLLPHVKQqnkCuVYMLMTraeTm5yhvqqqOCRUWvVWmDfRiPnb5KQN9h7PAHDuTPBci3pXlZULf4XhzGr7VS6gEJNrl9x2EG9vLds/PkU6qBPCOuG5ra6oErbj8f3a7r/lNe8/rSvZiveTnoBcraIRkF/ww6yVd7UKt2JPb5CoNO2BnuNJ7virWkP/XJUmYBjnYHo6RkYMrQk37BAHFQAkO6dGVTIZEc4oVUJIdc7W/feo7BxvWvaB2SGrVdVjWt5HqO/VzNVSjaDnvFSrtLFzfki9pBZKUZrvUHxuihlRNat3/sIWCbUxtEuy7DEUzv6Qq6JdWngIt2Y2R3pqfdumIPDnxtAp1AVjBOK/C1LXGDedixSl9AzdBM53fM6eVr7fJSODO+BqzysXpggdIjOqReSodYZDqTzSQss8dXILQvSerNwJVOu0+h8LWjq4Sp3ocCpt5Dq5DVsHVksq3V+Kf0iodMzomSsvlDBIbYijQJgTUU/FmRQt5/i62ert8W+XfyXi2dP6K42Utr/cIjDi57ayokrrPpMit5KtljnntOxnLRWN/sRDMu1ceRcIb+7IUMJwvX8vhONdvA9k5/Sc6f1nc5Ucw7gIYOTQmnDDDnFQYXYlk572ijtgap1SPXO86dkH4m1k5BxFUgHl0PSmpnQmtYRSeittzF4t1UpaQg8nhDNaSO0XAAHBU3Z6U0ySGc65fu+RgPsaUTVbWFSG9wqCh0ID3mGflWfOyV575I6hcPdHrzaNJIe0C+8r1C8QjLxG6AmdnDB/WjgLxgg8fv8vd41xy7lIpIm443NhV+DnLed/vmQk0Krv/xZzeOd8YKSlU6JWaXdsH9BppHnzeUmFR2qdYbnKo1CDKKV56rQsCNGmv3wAqqfTqmc+JamgUBxQ6q20kTsW5IZxaqnSBAID5OQM6RWFAe2d9VDCIK3BIeDt0H/3IXDk+/O39ZwQejWrnOICfdWXSkO0/alVGsltfy0K3/Bef6RI7T+jw+FQ+L93PXPOqc2Xp6WiUe657Vp5V2vArLTfQg3D5cI/uS97/G/zv+6oXSdsXqmWYZzLmVHlYGTYoTUsC6fTp6W9Uh0wtcnctc7xFs4+MGOOoslZafil4k9fKLCk8BAa16vh+LmP9GxHJ4QEarSEHqGEM1a/d7n9IuZfASYQzpOhXZIDAmwgvKpZtUopYf41vV8shFttqyXQ0fuFh/i99mvXCPf1axPyvtcaOmm9Npl9PGqZg9DfVe0a4fPvpasuhf+X+p0ThsETGUKq4/PzFu8iDf7VSsUFwNK7A++npVOi1rERfh/O0Fo5SuGT/1x2a2Z4bxNXn/l3mMOZQ0gp3Ok0MvA1pVZg/PeV0q+rp9MaynxKQjuEEFZMb6WNljDMv/1aw7OP7/W2U2iDsFiAfyBkxGqualV3evgHcYD3fasdX3oXYdibr69N4RLCSqntr5UwBFT8hYDU/gv1nFQbltqgJXBc55d6wrbWW8kp1a6GrfVVNEo99w+rQ2uDXHtCqWbzD+v1zAcYTmWk/zBx/+u50vQDQHBIqnZ/G1eqZRjncm4YWqMWlpk9abZcmKA2mbuWzplSdY7aPjBruFhhUVlQdY7Th6EB2o9lt0yyrjX0kApn5AKOiYsLA/atFe9dTxiidMyHWjWrpaJVbOWuUt/r6T3m9YZl4vZpeV9a2yX1Xld/fwSrvz8S8r7Xel3Tcm2y4lyUO49mDeuIFTtLA4Y7/7V3S7RJrBsUxgHKx7Fw3DphGDxR2OQ6PrHVvEGR2v3UOiVKlTKXjJQPv9SodRS1BFXiTqHcEKRw57DSG+74B4VKr6tnn8jd98tnge8/kX8NIDiEFdO6LbR0coW2ynWKe04EGrYKrKaTasPQBd454rTMqSa+j5bhdeLHGT2kWu1YVVuEIZzhl0ouGaltWPnQBUDzXsH7CfAG/YX/AQ5+I/86Ul8I+NM75FmgZbvoDeIA7/b4/v+03VfqWDFqfwlDycNdCEZv0Kl1WKzaNa24QD4k1dvmM39KV0Mf368+R6lw/7351k2hoBHDOJdz+9CaUAIpvZUYcp0wtcncAWBg+yTEVa0CAEGrHapV56jtA7OCVDcEtFK0HMtumu9KT6WNfzgjF3CIgzjAmveu51qi575agg89Fa3+rKoOlttXRgU6SgFSOO9RrY1yryt88aBlmL9R5M6jEZemYsSlqZJhrRSlY9P/d24ZBk8RqrjgfEVGqBNLaw2K5O539rR3lVSlwKNVP+nOYau+2tspKC6QmM9tQnBHUS2okhuiJhUshTuHVahzJ6m9rp6QT+6+4iBOIMynpHVS+3WzvUN7lRQXAI3TgF5/U54/zL+tUhWT2yWq9KTaoBbuKgUOSpWaUiuCDl2gLWjUQ+lYVTp25X4fquRLgeLN3v//9h3vUGotx3OXUcBP64MrFH9arxzECXYv81ZWSQ3R1jLkWTyMWs+w1JTu2tro75cd6veR2k5GDZcVnlvu/FBqg1p71AJ3tWGxDVt7jwela5rSYi2htll4XSDwSw61gE0I29v094Z6ZkyhECKGcS7n9qE1eoMjcec3O70pnh2RrvgaSiGP0mTu4teqPHNOcWiqPy37wKwg1a0BrZZj2Yyg0cxhdqFUWUkFHC0SakvORQaYH7LK7RcPAof8DU1v6ts/WtujFHzorWgVM2K7hLMSrhH7REugb0bgKPe6b206iLc2HVQMReeu2ovXbu8WUpvkKJ1H4vehdh1x899LinBaq7rUaA2KpO53YYb8fF/+wgny/MlVj0h1FNWCKqXOozhkC3dVQCC0Ybhqr7t7WfDvUrpLP0ZrVZpA6/xhgr0rvR1YrZPRy5E79rTsD7U2CIQQWy1wkArzpDr93y4Gyn4CBj6lXn2jh/A+9QxZVBsu2/V24PTvwQEZPPL7RwjiBHLzHYrlTw18nUtGAGnXBg67ViJUVvnaOUH7vF7+jxcep2cocf3m3n96tpOcS0Z4v5CQ2056hzgDQGIH4Jedga/Rf5r3/+W2jdpCMGrt8Q+HxftdbeEfYSi5EBaLSS0WIm6z0jBtuS8NxEPYAelrYZuB5/9fKqQfs8rYKRTCELVhXF5eHp5++mmUlJSgffv2yM3NRa9evexuVkjcPLRGT3Ak1fkVAgqlQE6tcybVKVUKRarFVsGBY9Kh0E3dUnBDRkrI81OFEmhIrXLp1g6n2rFsdNCoZ5hdqKGdnmBGLmzcfvBX2cdYEbLK7Rf/BRqWFB7Ckv+dj0YMV9RT0Sol3O3ihJVwpc5lf2bte7XXVQpF1+w5gsKiMsOvN3rOI6XriJv/XkYyvZ/J1q1bh5ycHOzatQtNmzbFQw89hHHjxgXc54MPPsAjjzyCH374Aa1atcKTTz6J7Oxss99KaJSquqrW0F8lpzUo8r/f2dPqQwUF4QR5ArXqEXGAphYyKnXmxb8LtbJNTM8wXLXXldseB7/xhh1S2zNtsDEVOLUSgN+PBt8uVym49T/aXnfIvPNVLEqSM7ydZ6nFCYSVSuWohYJq1Y5yQYV4u8tV36TfCpytFIVUI6UX7hD2s55FGNRCqvRbvM8rNYRXOLeP7lVf+VQ836HUYidSoWX9Ftrfi5jeeb3Ej5PbNhc0A349ENzWMavkt5Pc8EUp3y72Dtn1P3aE5wS0V5/68w/ihNfodtf5NorPj54Tgb5Tgp9Hqrpa6UuAJXeJAsoJ3v9q3Q8NW0sHYeXF8o87tg/YtCC81/X/uyRU6A6Z5/1CQwht966UnlJBeLz/tA020hTGvf766xg8eDDq16+PRx55BI8//rjZ7TLV4sWLMWHCBOTl5aFnz5546aWXkJWVhe+++w6pqal2Ny8keuYgclInRE9w9PzqvZLPITVxvJjeDphcR3vSB8oly1qDOKl2hRJoyAUGbu5wKh3LSseL3mN78eYizcPsrJqnTi5c6ZRyAd7aFDw3oVkr5UqR2i/Czznvbg+43YiFN+S2xfq9R/DsiPSA43vlrlJDw2cnrYQrnMtzV+0Nmh/NzH0vvO57BQclj71qsVVkV8UNpTrO6L9NatcRN10Tjea0z3R6P5Pt378fV199NcaOHYs33ngDX331FcaPH49GjRph2LBhAICNGzdixIgRePzxx5GdnY2lS5fixhtvxJdffonu3WUqjeykVEmxbmZoVXJagyLhfnJDoeTCDK1BnvAc4lBQrXpEqgOpFDLKdeblQjYzFpjQQu511baHnuG2WgnD/gDp6qZw5sLqOVFbECfo/ZB0SLVupndYmdSxr2U4oNqKnXpWWpQ6vgpfl6+0CWU/+/M/dtWObf/z3f/9dRqpPswRCNwOUpVEjWU+81ZIj9rQTGpeL7lrivhxnUYCra8C9n0e+DtxECd+jFylpnj4ohKltqlp1C5wwQ+5IFpqqGdKd2/Fppb58/z/bkh9CSAOxAD94f7H954//oXpBsQVkP7kAk+9rysMYVe7HsnNtWfjgg1iMR6Px6N0h7Nnz6J69erYvHkzunTpgurVq+Oee+7Bs88+K3n/oqIixwda3bt3R5cuXTB//nzfbWlpabj++usxY8YMTc9RUVGB+Ph4lJeXo169emY11VBGBApqw7ZC7UypPbawqAzZeRtkHz/nxk4Y2iVZ12uqtUfp9aT8tXdLTAoxoJF7vVnDOqJabBXZ7S31mKXjeziio2lG8Cs85+mz5wK2i95jW2m+P/GxZPV2FrdtaHpTXN6mEdbvPRIwVHVoelPMURmiLZDaF0btnyVbi4PCOADo27ZRQCATyvVHap48QHrbG3m8yb0n8bEhfk/hXAO00PoejdwWSsc/ANnrpJ7zwy2LshjFzs8PTvxMp/cz2aRJk/Dxxx9j9+7dvtvGjRuH7du3Y+PGjQCAESNGoKKiAp9++qnvPoMGDUL9+vXx9ttva2qXpfupuEDbUK8xq8zrQMi1Qctrbn9HelEAcSfTvyOp9J57Tjw/REupvf7VKP7/H+68e0bRs3rh1v+od/CzX/I+l/971TpEUI6wf4MCGIl9oHacKk3Qr4VSx1rqOJQ77gSt+wMdhwe2RypoOlGiPEF+9kvnq2jk9pN/+5T2u9p+7j0ZaNBCfpEDtWNb6v2lDVbeb/77Wm4fD5kXXgAlZ8wq73/FVXjH9gE73gsO2vzbI1RB6XktLUOexXNYhqNxe+DwruDb/c8VQN82F+Y0FF8D5faxsI39jx2l+0tp1hM48JX87806PtJv9QbeRr+mmX9Loe/zg6bKOP+8bsmSJbjxxhvx22+/YcGCBYiJiQEAnDhxAk8++STmzp2L33//PYzmm+vUqVPYsmULJk+eHHD7gAEDsGGDvvDFTYyYbFupwxRuZ0qtUkFtRUejq1HUhmkJHriyNZo1rG3aRO3+lXhah8mt3XPY9oo4MzrXUs85tEuy7mNbbb4/8bFk5HBELSGJUrVkdnpT9GrTSNe+ldpuADTtHy3tlTv3/Icrhnr96dWmkWQYJ7Xtjax2CmclXDNpeY9GnXv++16pelmuOk7r+eGmRVkihZM+04XymWzjxo0YMGBAwG0DBw7EK6+8gtOnT6NatWrYuHEjJk6cGHSf3NxcQ9tvmOQM+RVK/Zn5bb5U5Y94dVQ5SnN++RMP/ZMa3uQ/QbscpdAmlHn2zCA1/EuuXeL7yvlhdWD41HNC8Da8oDnw60/a2ykcU/6rDQLnO+zi+yoRJuiXmw9KTf/p3mHZSisj+gdS8Spfwu/L9/4DzodSUvPK9Z4sXWEl8D++Y6tJ30don9IiElqqCuOT5YfPyVW7Cttaap4uobJP6txu1Td4/8jNZxdbTdswUrnFPIbM87ZRHPiKK78u7OpdeVWJeEi8FPH1VOsw9OQMb8WVsE21DPFVIhXEAcGrW0tVrskda8L78n9//nOkiYnDxTN/ylc6ylEK4gDgm5f0PZ9WXW8DfvtFOhwN9TVtXrBBTFMY5+/aa6/F8uXLcd111+HkyZN47bXX8Oqrr2LatGk4fvw47rjjDjPaaZijR4/i7NmzSExMDLg9MTERpaWlso+rrKxEZWWl7+eKigrT2miGcAMFpQ6T8P9SvzO7cwyYN1zLv6N9+uw5ySGq4hVWQ6UlTNQ6TO65Vec/LNlRYWJG51rpOfUe20rBrtSxZNRwRD0hidzwTy1Dsv3JbTcxqf2jtb3pqfVVA5lQrz92LUaiZ/i8k4Y8GnXuSe37peN7SIaO9/VrI7nvte4jt67+HCns/kwXymey0tJSyfufOXMGR48eRZMmTWTv49jPeeKJ0eWqKfQsMBCK/tMDq4S+fQf4o0w9INO7mIAQEIQyVFRtaKLaKoGhhER6n0cqXJOb/09rEHfJSO/+ED+n/8T7SkP7Wvc/H0z58z+m/IMRqaHRP6xWbqMwPE0cqPg/j9r2b9NffmVEqTBLPORPzle58mGi8HqXjAD++DV4bi6ti38orVp5eLe28+Pje72rk/ovEKC0zbQEfMKE9+KwVbLyTqYiTBjyqragRUIb6SBMGLLsf74DwdVZSkFc78nesFItiBMq/aTmh9MqOUN5NdBwiY8jqWthcYH848XXDKVKPvHvvsr1hs9G0rLyrF7CuSc3hD2U1xwyzxtE6lloyGRVQnlQnz59sGrVKixbtgyNGzfGvffeix49emDnzp146SWTklGDCd/+CjweT9Bt/mbMmIH4+Hjfv5SUFLObaKhwO7VKHSal3xlF6Bz769euEZaO72HqsLD01PoY2iUZIy5NDXp9I0NAqfcnxX+bannMi+t+RGFRWdjt00Pr8VBYVIYlW4t97RP/rPU59R7bcrfPGtZR8liS2s56971cSKK0b4w4r/TeV9gHcvPpybX3vn5tJG8XtnWo1x8jtj2gfGzJmZyVhqXje2DOjZ1Mv874C6WtAiOOGaUAd2iXZMmKxHD2kVtXf44kTvhMp/czmdT9xbe75nOeVAf+8C5vh9afFd/mFxdId/L+faW306+k/3RvR0crIRgRJhg/tk++81lc4O08CaGE1ucWy5/qfS9L79b2nqReX+15pLahYN3MwPsr3bf35PP/xqzyhqJShAUOOo2Ur6TpPRm45f3zk6QL/I8puSBJeM9KbRUTByrC82jZ/kKwK7ZpgXQwcuR77cHC958o//7bxd6O/5hV3qGpY1YFD9WVap+wHWXDvtnyAVL6rdLtELbRy/2UjzUtYdHx/d777l52fg5Kqe0v1/42AwPnpus0UrpyEvAGtlIrrgrnj/B4pe0lp0EL+WNcMGTe+X3m/1p6ad22Si6RqXCUqjiWWjDj2D4g+VLtrydVHZcovdiWbBVoOORWfg6FeD/KVf7VaaLveXcvC+1vgIlUK+OqVKmCqVOnomnTpr7bCgsL8Y9//AMnT3o/4F9++eV4//33ERsba15LDZKQkIDY2Nigb0cPHz4c9C2qvylTpiAnJ8f3c0VFhasCuXBX2Aylw2REZ8p/qJTdixKY/fpaKvGUhskdOHYyoCpOYHWFiZZjRVx50zklHtsOlvt+FldhKT2n3mNb7v4jLpWfFyncfR9K9Y8RIYWe+67fe0RynjR/cu1V2wfhXH/C3fbhDNtUq3ozel7EcIeYGnHMhHKshrOPwv3bRPo47TNdKJ/JkpKSJO9ftWpVNGzYUPE+jvycJ9chbdUvvMoOI9sCqFecAeodZX9CZYjSsD6p34tDSqXn9qdUtQTIVwxJvb7c6nxaAwbh/kr39W+HUsWS/wIHclVbQnCiVIko1xZh+GW4i0VsWRQ895PcMSU1nFQpCOx4A9Bnincf/rjGOxw6VMLE8EBgYOwfloi3I+ANm86eln5Opaqlek3lfwdIB5vCNpMbUiomBHBi4kVW5NovLPLhT25Yu7h689vFweHc0AXe/9db6Xv2tPLwSr2LhsgFYMKXA2rSb/Xuv3NnpIeydhsbvKruJSOBoaIvucTXGLWhulLbGfDup94PBZ4HZlSsyWnZV9u5l9Lde1+l1Wt3Lwvcl3LVcb+VKA8xF5OqElT7u2Yy1TAuJiYGU6eeTw1vuukmvPvuu0hKSsKrr76KNm3aYPDgwbj++uvx/vvvIy4uztQGh6t69ero2rUr8vPzA5a4z8/Px3XXXSf7uLi4OFvfm7jTF0on0MwOkxmdKbmOqZ2dNKnOuZEdcv/n33/0pK5hcoVFZZJhnNaOuFHvQ+1Ykaq88Q/igOChdWrPqffYDuVcCGc4YighiREhhdxzeBA4XHVoelPfvHRKlNqrtk3Dvf6Esu1DmU9Qa/uMnhfRiCGmWs69UOcA1FLFGOr5YfcXLdHEaZ/pQvlMlpmZiWXLlgXc9tlnnyEjIwPVqlXz3Sc/Pz9g3rjPPvsMPXr0kG2LbZ/zlIa9aV0R1ey2CNTmrNPaub5kpPe5pIbu+XeOpAK0bxcrd77EFYRCB/v4fun7i+dT8h+eKff6UoRto3Ub+Ac5Wu6r5Ktc73PFVgsOC4VtDYS274Tbwx0iLTcJu9QxpTf48w8WlTr4/tpdK10pt3dl8NBhuWG3UnPEie8rt1Im4D1W5YblKhG2j9zzDpkHlBdre17x8R/0XmUqcosLvMGY/0IEx/ZJh0T+hO0qfNGgZa5MgbByZ6hzTfpT229aqrzkjmnf79/wPm/v/82JKg76iwukQ2qlIE4YZvlHmfJwar3HVLi0HstCGFlcoHzfvSuBj+7zzhkn/B2UO5cqTygv9CBQWrXWyWGc2LJlyzB16lT87W9/Q82aNQEAq1evxqBBgzBo0CAsW7YMderUMbyhRsrJycGoUaOQkZGBzMxMLFiwAEVFRRg3bpzdTZOkt4pIiVkdJqM7U26Z1NvMVQD1btNwwhuj34dS27UOmRNX4qhtD73HtpVzfYW6b4w4r+Sew/+2tXsOqz6PlvaqbVOr51fTU+Wl5xww4/r0/Oq9mtuqRG5/65kDUOuxauTqrk6aey+aOOEzndpnsilTpuDnn3/G6697P2iPGzcO8+bNQ05ODsaOHYuNGzfilVdeCVgl9YEHHsAVV1yBWbNm4brrrsNHH32Ezz//HF9++aWp7yUkUhUmdk0wrTb3m1ogI/de0q49X3n2c4G3w67UaVerxoqXqVhMvxVo3O78cDgt82lJdc6EQFBr5RFwfttonT/v7Gnv+0vpLl1N4t9B1BKE+Q+DvGSEt7Lyh9WB21ppLje5du9edr4zLLdvgwKdDO9+1kLqvekJ/vzPFT0h3uUTvftAav+LwyG56jTh/8X3Fa+UKfUaQ+adr/zRM98ioFy5ldJdX4WquG3i9kvNWSdVzSq36IQUcbWc3ByZF2UB//008Lavcr3nuVCVprZistR8e1Ihu3gfh1NdKdjymvef4Myf8qv6arV7WeC5LgSRwPl50PRct0IlnPviykKpwEtqsRAt18nC173/hOuUXHXcwW/U99clI7wBsNTjzZ6LVYXuMG7v3r1ISkoKuK1z585Yt24drrrqKvTr1w+bNm0yrIFmGDFiBI4dO4bHHnsMJSUl6NChA5YvX45mzZrZ3bQgoVQRmUmpw2RkZ8qqSb3DqQazIjDUu01DCW/Meh9ybddaqdcioXbQ/nFzhz3UYM2I9yz1HMJt4pDG36xhHVEttoprq5W0VnnpPQeMvj4VFpVJLoIg1Vbh/krHkXh/631/Wo5VreGemV9YUPic8JlO7TNZSUkJioqKfPdv0aIFli9fjokTJ+KFF15A06ZNMXfuXAwbNsx3nx49euCdd97BP//5TzzyyCNo1aoVFi9ejO7dDZzTxkihLGRgZlv8F3EQaA0I5d5Lcoa34kjLcCK1aqxaDaVvFzpvgL6KGyl78+Urj9RWahRvg6AVIzPUJ6H3f+96F8j4djHQvJf2UElou9xqo0LVXdpg6X3rv/qkcLuWhSmUjqnEjtJD7IQqI8A7mX9stfPhq9ZOtfC6aYOVh5AqUQr+tKyU6T8Ez/94Ec+5Jl6gQu081BJMCOQqhYT2FxcAb94YeB+1Ydp6g0VAfsXRJp2CwzggsALqUKF8VZzcEHi9lZe9JwNl+8O7ngD6F/OQIt5fe1cCNS8Iv21aiENaQD5cFIaiKoWl/ouKKFXJ+R9fSpWmSuS2jwNWVtUdxok/tAnatm2L9evXo39/mQkdHWb8+PEYP3683c1QFWoVkdtZMal3uJ1Ep64CqDe8sfp9SFXeiKs9/9q7JVbuKo24TrzTwkSpkEagNo+e0wmBVXZ6Uyz1G4IrVeWl9xww+vok9/r92jUKq4JP7fmVznGlY1VugQ9xuOeWCmfA+Pn/3MIpn+mUPpMtXLgw6LbevXtj69atis85fPhwDB8+3IjmWcPqIaly5CbqT7tW+TH+QYzUe9G6AID/RN1ynfv1/1KfV8mszmmbgd45r9Tm8/PfBkLwo7biqUBqqG3VGuergbQEA0rbxp8QTCgN5fVvr3hOP4H/+9Wyr/0rw/ypVQwJnfv8qdLtkgthe/3Nu9KnXHWXQG7VWTGl4E/LSpliwvbrNPL8sSW1GIL/pPahBF8CYbijXKWQ3PZRG6YtvFdxtaRecosfiAkr+IqPS7k5Ihu2Vp53TkqDFkDfKef3i9w5PGSe97zzr4YTC2e7yAVR4V7r6jTxzr2mRGk+PqltffAbYOBT2la17jvFWzWodCwLx5dcdZwWev+uWUR3GKekefPmWL9+vZFPGfX0VBFJcWsHw+xJvbV0EpW2XWFRGQ4ck+7gmrUKoFn70o7VDKUqb/zfHwBk520IeIxTO/FKnH7+yYU0D1zZGhP7t7W4NcYRB1bZ6U3Rq00j2f2g9xww+vok9zriVWpDDbeMPMeVKinF4Z5Tv7AQY/WeNH6mi1JqE/mLqS3AoPa8gLcTu3vZ+Y61f+daWJhA3Pn1H053fL+xcyQpzX8kDAnTG54K998uMzy392Rvp18c1khVmPWc4F3pUykYuLCrcigg+GG1d2VBrbRMeK5WeSTVsS8u8FbIKHXIhZBSaTEOYXEA8TZb/6/zwynlVspsfZW2IM4/LJVaxEBqjj4tx4t/QNGwdfB++XaxNxASnsc/5JM7B+TmxoutJj/0GNAf8okDyFACk3bXAokd/hc2q8w9JyY+LuWOQbl555SGVvsPQfd/fqlqx8ZpyuddKNul6+1A+i2hP17NbyXS1b7iYahy9sqcM1r/ZgjD6nv9TXohDMB7nRJWxlULobXMH6fWRgsZGsYB8t+yUmikOn1iUtUTgPs7GGZO6q3WSVTadkqdUbNWAQx3XyqFQmYHn3LElTf+Py/ZWiz5GLs78XZO8G8GuTCmT9vGpryeFeGkVGC1tPAQbs1srlgFpvcc0Ht9MuIcDDXcMuocV6qkBIKPJzuCfr3cVL1nB36mi0JqE/n7UwpFxB0cuee9ZKS3AysOlPyfR24OLP/hdFJBhNahqsKE98D5yiup+Y+khjQJIZL/Y5XIbYey/d4KEX9yQz2FbSMMhZQLBsS3iwOH1v1Dq6oJdSGP3pMDt6/cMF4xIYxQC1qEdg1d4B2mK3VMNWwNfPOS5MNVh1CL2wFIDDH1m6NPLpiWmsdMHFD4V4hKvUeBEBDJnQMXDZIO447v9z5GqmpPLjAWqA3Tlts/wvbbtED6uPv+E+m2AvLzyvnTOs/iV7neMFv8vosLgivX5IYxKg3HlwuLQh1i6X/MhVMNCcjPUSm3erfa9UxpOHrD1tIr1kotiiM8h1zFs38QLfcFDeD9e3Ld80CtBtq2k83zxQEmhHFkvMlZaYirWkVypUwguHoCiJwOhlnD+uQ6g6fPnlPcdsL/iz1wZWv0advYlLaGuy8nLi4MGKYnFQqpVapZfczI7Z8Dx06isKjMlmPY7gn+zWBlEGtGOCl1jIYaWCmFa3Lngtbrk5b3riXcCyfcMuLLDaVpE6SOG7uCfj3cUr1HZBk9C0roqaKTel5hZT25zr/aCqVKiyb0nOgd0tftLuWhYVJVWlLBiNS8VOL7+a/EKpAawisVEoqrntSGevpvY7lgQOp2/86zXBWYUKW34z3pgEqoUpEivF+pwEYIG/VOXn9h18BqMy2BsVyAqzZEWIk4iAPOv9+zp+XnUgPkg8eeE6Tn6pM7XuXeu9w5IBXKAt5jdd3M81VJ/seNUkChZZi23OP9t1/ZT/oWSVAL4sSvq1ZBtTc/uBI1OSNw/sOzpwPnJBSTq3b0P++E51BazCP9ViClm3y4JBX+qs2zBnirDH/Zef5nodrt31cG3zeU1buVgrieE6WPdbUhwj9vka9s87/mSR3Xwt8TwLudqtZQ3kYOmC8OYBjnGn3aNpYM44amN7VkgvFII1dxOOmDHejXrpHkY5Q6os0amhdYhbMvxUEcIB8K+QcLdld1ye2f51btw3Or9lneHrsn+BfaYEY4amYFqsCMcFLuGA0nsJIK1+ReR89KolLvvUVC7aDFMdTCvXDDrXC/3JDbhrOGdZSdX9CK4ysc6/dqXziDKKJIVecItC4ooaeKTvy8/h3dUMM2pUUT5DrYwnPKvTepyo29K88PT1W6HxBY0Sc3HKt+C+n369/ZVBvqKd5mch1pvXO5Ad7qNUC+UkwcHArk3q/aSpZKxItdCGGn2vGgt+JFrmJI7vkBbaGi2hxhX+V6QwMp4jBFrlpOoBbKSgU4/lVJQjB4bN//huxK7H8tw7SVzlfxNpNbqEMvcWgFKFdQ+W8HcYCenCEdJElVOcqR2z5yXxoAyuGS+Lm1LEIx+Lnzz+t/PBixerfStUSogBWHfl/lequQ1dRrKn273rkYZacamKytitkiDONcQqoTNjS9KeaMSJe8v1xHYv3eIxjaJdmUNurhhLm0hI77pA8C/wjoWdVQy+/CFWq4UFhUFhTECZRCIadUdQmd+LV7DgcF0Va3x+4J/s0OR81eWMKIcFI8p6DSMWpUNZbcubC7pALr/nvUd5vS/pB77/7XHT37085wS27bqi304bSFSwRy10i5L7mIIoaWed60VEkodbrlwj65jq5U1ZyWsE1rm8W/k7uf1mo/pc6w8Dul4VhS/DubSmFSqBUdWjrwwnOrDVUUbw+54Wfi0E7rSpa9J3tXS5Ubvqx2PMhVIMoZ+FTwcXnJSKBVX+2hrZRw5vgSgrgLmgO//iS/WIE/pVBWbdt/lRv4ntRWctUb6EttMy1B3CUjpeeQ8w8Mv30HgCc4/JWrDPQnHlqvZ/i9XkrHrZ5VtdXCZv99FeqXLUqUjqU2/eV/H1tNfahtm/7BCzrIXfNCCYXF0wHYjGGci+jphKWn1g9aRRBQnzvJCnZXXfmrFltF8va+bRthzZ7zoZx/Z97qYVehhgtKlXxKoZCZVZV6Q9j01PqOqPJUGtYsxYpAyGlDXpWEG06KrxlK1avpqfUNC6zkjj3/IA5Q3h9a3qPcSqRKc8zZ+SWGkyvd9JDbv5e3kT6+iCKC0R1NqY6dUtgn9/pjVgEnSs6HJ9++A9RNCnxcOJ1HrbRW+yl1hn9Yrf91xeGjVEcypbvyCoVq5NosLIShdaii1O+1hphaKtaEDrPa8GW1wLhVP21hnNDRT87QHlJoCRW1zhEmFT74+/WnwJ9DPV/1Vgse+V762ABCC/TltpnU3IzixQPqJgUHpeKAzj/svmTE+cU8tCx0oaUq1ajJ/vV8aaD0HOLrQ+v+QMfh2q6ReoekiinNAaoWInYaKZpnUWL+QT3nohIjgkeTMYxzGT2dsF5tGkl+62/nUFWnBQtyHeX7r2yD+69sI9nhtKMzGspryr03taoPsyZdDzWElQu8jKhG1BoOKg1r3n/0pOT7MDsQctOQ83DCSalrhpbqVSMCKz3HmNz+kDt2lB7vpC8spDi10k0vNywwQWR4CGVGR1M8FFIp7JN7/b358nNuhTtkTA+pTq5UB1NpTqpvF3sXEFDjPzRSHD4CoXUklY4XuUoR8Zx5cvf1f4z4ueU652dPe0M1/zmppNogtXKj3mHQeu8nNReg1pBCS7AJqIdx4vCh8A1tq+CGcr4q7VM5wiIp/kIN9OW2WdN072PFoZ9S1dixfcorrgrXEiGQE7ax3EIXWqpStR53Vn1xYGfQJHedFIbVaq2a7jRSfv7BcANDo5/HJAzjIlRhURkOHJPuxNvZ0XBasKAWEiitvhjO6omhtlXP8+gd2qz0uHCr/0INYeVWrjWiGlFv4CE3rFnpfZgZCPnfLj7WnDAMXCzUcFLumqFUvWoUrUEaoHxd9X/vp8+eCzqG/B/vtC8shDbp2W9OOf7U2uGGBSYoymmpPtEr3I6mGrWwT+/rbFkUPJm3UUPGxIROYtpg5So9gdIk4VqGY4nnKJN6X3o6klqOF60d+OIC72TrQrjkPxG93HAx8fuVm+9NaX4/tefUM0RXLjCQG3oqRypc0Rpsag0ehecEtIVxoZ6vQau/qlQOSr1OqIG+XBgonD89J8gvDCI8Xs85LzVMWssxFc5xZ8Y1W4mdQZPatURP1bSDwzKzxXg8Ho/djXCjiooKxMfHo7y8HPXq1bO7OQHkAgzA29GYZFOFRWFRmeT8XwCwdHwPR3fa9HJSZUuo783IbbJkazFy3t0edPucGzvJzmFYWFSG7LwNQbcrTRavZ1J9qedWOw5DeR9GEB9P/uex+HedU+Kx7WC572enVVXppbSvAFgS+izeXCQZoAn0XleV9qfcMXZTtxTckJGieSirHkrPo/da5pRrn97Vj60MD538+YHOs30/FRdIr3o3ZlX4HZegDtHE85OIh0tLu6VeX26VPznZLyl33PXSMhm/1LZXe79CkCMOPuSGMIb6vow8XsIJFPxXopSaOD+U9oRbaRTO49W2hZbn1vv6SqtUAsafr7Irvcq8TrjHWnGB/Gqgeo4PLees3Plkxn4z85odCaJo++j5/MDKuAgjVVUBAA9c2Rp92ja2LfBSCwjtrkQwctiV0ypbQn1vRm6TUIaDyVVEyc3zp6fzvXbPYdnXlHrPQmfdzCGzSuSqyqSONf8gDrC/qipcoVavGmnEpanYf/RkUJXp5W0ahRTgKFUJyh1Lb206iLc2HfQd10aFXkrPo/da5pRrn952CNe6wqIyLNlabHtFHxEAc+ctMnN4k5aqErnX1zOEzqhKPkD7ZPxS217t/QqVK+LhWIB0GHd8v7c9eveJUcdLuHMKCu9Xbb43PcKt/gn18Vq2hdxzi4McPa8vN9dd19uB9FuMP1/934uW64IRFYtGHK/+15Ed70mv/ip3ndCyT/TuN7PnmnM7bh9JDOMijFyA0ayhfOfC7KoApwaEZnHaUFwnkFpQRC2E1RPg6el8KwXDUs+tVnlmVZgsFY4qLdIhvp+bjz0nLBpgdBvkwm61obEvrvsRLRJqGxJ6qZ03eq9lVl371P5mhdIOp1T0EQHwduSP75f+nZ4QSm3+MCM7QP6vFerKp0rDPv2FupqoXHu1rvApt+21hpvi9yw3ZG/dTP3D24wafmxUh9ns4dBWCHVbhDtUUW4bGR3ESdF6XQg30Dfq+PAPu8UVhUZcJ/SIhGPeTNw+khjGRRi9FUhWdEBCCQjdjJOCB5v56e6AIC47vanqsD61iij/DrnWzrdcMCx+bqX7bztYjlnDOqJabBXbK2i0HlORcOw5YdEAq9owOSsNv1T8KbkADwBsP/ir5O16Qy+180bvtcyKa5+Wv1l62+GUij4iAMpDr9Q6l4pDziaYN3eRkfMAtekvHcbJreoYCnF7Lxmh/hi1bR9KuCkEGlJD9vTOixdutZLAyJDEiPbYKZRtYcRqxW7ZduEE+ma8x6EL5BcDsIJb9ptduH0kMYyLMHompNbTAQmnei7awilOCh5I6jhbWngIt2Y2V90mctVI4g55dnpTyceLjzG58OGBK1tjYv+2QbcrDZU1Yo64cKtSpY41uyr3yDiFRWWyQRwAdEq5AG9tOhh0u9wwajlq12a91zKzr31a/2bpbQermckx5IZL9p7sDan0VOOImbnoQbjhgz+tE+P7v77eeZ3E7f12MdD6Kulhblq2fTiMGrIHGDP82MgOs52rPRohlG3hpH3pdGa8RzsXNACiY7+Fg9snCMO4CKR1OJXWDki41XNyHSMAETs/jxOG1enhHwoBxk6KH25HV1yNJBfuaRkGKxc+9GnbWPJ2M4Nko6pSpY41p6xmSaFRGn78194tJeewA4BJH+zA/qMnNR9HWkIrvdcyM699eq4letoRbV8YkYPJdeQbtFCviAt1zrNwmTEPkH/FGOANw/zJLYqgpfpPrr3xKdK3q217Ixg5fMuIMMLIDrPd4Ui49G4Lp+1Lp4vE9xiJ78lI3D4BGMZFKC3DqbR0QIwaviPuGK3cVRqwQmKkzc/jpjBEaQ41I/aL0R1duQ55rzaNcGtmc8Xt7pRKH6OHxYnPdycM6VTilPPDKe0Qkzs3/FcSnpyVhhYJtYNWedV7HGkJrfQeT2Ydf+v3HpG8XW57aW0Hq5nJdv4rUEpR68iHO+dZOMyaB8h/mK3/HGpKFYBaKvLk2nVhV2DLa8r3D3dVTzlOHL7FDvN5eraFE/clETkWw7gopqUDYuTwHf8V6yJ5fh43TQSuNIcaYMx+MbqjqxTuael8O6HSx6xhcU4Nl/w55fwwux3h7Au5c0YI4gRyKwvrPY6sDG9D3S5yQ3eHpjc1pO1uq2amCCIOly7sCvy85fzPWjryWoIvswIBM8IHuaGvDVurVwCqVeQpDYM9ti/4dsC7MmgoVXh6cPhW5OC+JCKNojqM++STT/Dggw/i3LlzmDRpEsaMGWN3k3ys6lSrdUDMGL7j1Pl5jNjmbgsatazGacR+MbKja0S4Z3eljxnnlRUhV7jniFPOD7PbYcS+0HLOuG14ZTjbRe5adXmbRqqP1XrcOr2ilCKQVOj08xb9ixXIBUxp11oTCBgdPshV+vmHlHK0BJNy7RXfvnsZ8O8rpZ/DjDn4nFaNZlYlYDRw2r4kIkeK2jDuzJkzyMnJwZo1a1CvXj106dIFQ4cORYMGDexumuWVI0odkHCDD6lOkBM7kEZtc6cGjXK0bHOj9ouRHV23V7EYXS2oNVwKJ0wz4hxxyvlhZjuMDPqUzhlhX2qZK9EJwt0uof7dcEolJpEkudApthrQaaS+55ILmKwKBITwobjAW0kWToCjdyipQE9FnlxY4v8+1Krw9uZHbuAit0IuEREZJmrDuE2bNqF9+/a48MILAQBXX301Vq5cib/85S+2tssplSP+Qg0+5DpBTpufx8ht7sSgUYnUvvCnZb9YUcUp9Rpur2IxMlDUEi6FE0oYdY445fwwsx1WBI5Sqwn3atPI0cG0EQu56P274cS/p0QBQp1vTa5iye5qHKMCHKlKv0tGSg8lvWQk0Kqv8dVbWubhWzcTOPNn5IVURq+QS0REklwZxn3xxRd4+umnsWXLFpSUlGDp0qW4/vrrg+6Xl5eHp59+GiUlJWjfvj1yc3PRq1cvAMChQ4d8QRwAJCcn4+eff7bqLchySuWImN7gQ60T5KTKJqPnxXNS0KiFeF8AgaupKoVtVlSdRHJli1GBolq4FG4oIXeOvFdwEAA0vwennB9mtsPswFFuNeFbM5tbPtRXz/XbiO2i9++GU/+eEvmEMt+aOPBqMxDo/ZD9IYnRAU7/6cCJkvPztH37DlA3ybr5uLQuQBGJIZUZK+QSEVEQV4ZxJ0+eRKdOnXD77bdj2LBhkvdZvHgxJkyYgLy8PPTs2RMvvfQSsrKy8N133yE1NRUejyfoMTExMWY3XZVTKkfCpaUTJBVE2DEBvdHb3ElBo1ZSq3ECykGYFVUnrGzRRi5cAoAlW4tx4Fh4oYTcufDWpoN4a9NBXQGpU84PtXaEei0yO3B0QsAUSkBu1HbRE2BHyt9TinB6wiWpwGvvSu8/u4cRGh3gFBcELpgABAZfZodCUkFpSnfg4DfB9420kMqsFXKJiCiAK8O4rKwsZGVlKd5nzpw5uPPOO32LMuTm5mLlypWYP38+ZsyYgQsvvDCgEq64uBjdu3eXfb7KykpUVlb6fq6oqAjzXUhzSuVIuELpBNlVAWXGNnf7EEpAPQizIhRwQvDgFuJwaeWuUmTnbVB8jNZQQm04s96A1Cnnh1w7wr0WmRk42h0whROQWx3ESh23/dqpL/hAZDmt4ZLS0EktFVpmTshvdIDjhOoscVAKSC/o4PSQSu9+N2OFXCIiCuLKME7NqVOnsGXLFkyePDng9gEDBmDDBm/ntFu3bti5cyd+/vln1KtXD8uXL8ejjz4q+5wzZszA9OnWfOPolMqRcOgNuOyugIqEbW40tSDMilDA7uDBbYRwSep8EtMbOAvnyHsF3mo4sUgJSI26FpkVONr9hY0Rc79ZeZwIx+3cVXuxZs8RrP7e+y+ShrtTFFELfZSCKrMn5Dc6wHFKdZY4KHVbSBXqfrdqODARURSLyDDu6NGjOHv2LBITEwNuT0xMRGlpKQCgatWqeOaZZ9C3b1+cO3cODz30EBo2bCj7nFOmTEFOTo7v54qKCqSkpJjzBuCcypFw6Am4nFABFQnb3EhqQZgVoYDdwYNbyZ1PD1zZGs0a1g45cBYeIxXGRUpA6oRrkRo7vzxwa0C+Zs+RgJ853J1cSSrw8icXVFk1Ib+RAY5Tq7PcFFKFu9/tXhCEiCjCOSaMmzZtmmrl2ebNm5GRof2PgngOOI/HE3DbkCFDMGTIEE3PFRcXh7i4OM2vTV5aAy63dvAimZYgzIpQQO9r2DHvoNPInTd92jY2ZJv0bdsoINyIpIDULdciu748cGNA7oaAlUgzIQxaN9s7V5xAKaiycsinkQGOU4Mvt4RUThjqS0REshwTxt17770YOXKk4n2aN2+u6bkSEhIQGxvrq4ITHD58OKhaLlo5LbBwYwfPDcLdz1qCMCtCAa2vEckrr+ph1vkk3r792jXCff3aRNR5ymuROrcN63dLwEqkWXIGcPO72ucCC2fIp5HzzIXyXG4JvpzIKUN9iYhIkmPCuISEBCQkJBjyXNWrV0fXrl2Rn5+P7Oxs3+35+fm47rrrDHkNNzMjsDAi3HNbB8/pjNrPZoRtZoTBds876DRGn09S23f190dwX782YT2vE/FapM5Nw/oZsFLE0hpUhTrk08h55syes46COXWoLxERAXBQGKfHb7/9hn37zpde79+/H9u2bUODBg2QmpoKAMjJycGoUaOQkZGBzMxMLFiwAEVFRRg3bpxdzXYEMwILI8M9N3XwrFBYVIa1ew4D0DfE0MnBlFnVaxyKFszI8ynati+vRZGFAStFPS1DPv0r1wDj5pmzas46CubUob5EROTOMK6goAB9+/b1/SwsrHDbbbdh4cKFAIARI0bg2LFjeOyxx1BSUoIOHTpg+fLlaNasmR1NtoxaxZHRHWonhz5uJw6tnlu1T3Nw5dTgxMzjhUPRzMXtS27HgJWinlIlnbhyrc1A6fuFMt8Y5y6zF4f6EhE5kivDuD59+sDj8ajeb/z48Rg/frwFLXIGLRVHRneonRr6uJ1UaAVoD66cGpyYebxwKJq5uH2JiCKUVOWa/+IQ/kKZb8ysucuMnM+OiIjIYq4M4yiY1oojozvUTg19wmX3AhdyoZXwO7U2OTU4Mft4sXIomt3HiB20bt9o3DZERK4lV7nWZqD2FVuVmDF3GeegIyIil2MYFyH0VBwZGVg4NfQJhxNW5FQKp5R+5x+COHGOJCuOFyuGojnhGLGL2vaN5m3jNAxFiUgTuQq13g95/xlRfWbk3GWcg46IiCIAw7gIobfiyL9DHW6HzYmhT6icMgeeVGgFKAdXciGI0/aH248XpxwjTsRt4xwMRYlIM7XKNaMCLqPmLuMcdEREFAEYxkWIUCuOjOqwaa1GcnqlhlVz4GnZDkJopWU1VbeFIG6eSJ3zJMrjtnEGt10PiMgB3LTqpllz0BEREVmIYVwE0VtxZHWHzQ2VGlbMgadnO2gNrRiCWCeS5kk0Ohx38rZx+hcBRuL1gIhC4pZVN82Yg46IiMhiDOMijJ6KI6M6bFo6uW6p1Fi5qzToNiPnNNOzHfSEB04OQSJNpMyTaEY47tRt44YvAozE6wERRTw3VfIRERFJYBjncGZWcxjRYdPayXVDpYZUUAYAA9onGfYaWreD3vDA7BAkmqqKtOC8d/Kctm3c8kWAkZwaihIRGcotlXxEREQSGMY5mNnVHOF22PR0ct1QqWFGYCgOsbRsh1DDA7NCkGirKtKK897Jc9K2ccMXAWZwWihKRERERETnMYxzKKuqOcLpsOnp5CoFf06pujI6MJQLsdQC0HDCA6NDkGisKooGbgjHjRJN71XMSaEoERERERGdxzDOoays5gi1w6a3kysV/Dmp6srIoV1KIZZaABpqeGBGqBmtVUWRLpqGMbrhvTrlCwkiIiIiIrIGwziHckM1RyidXP/gz4lVV0YN7VILsZQC0FC2q1mhphuOQwpNNA1jdPJ7ddIXEkREREREZA2GcQ7lhmoOwLphrlYyYmiX1rnh5Labnu1qZqjpluOQQhNNwxjF79UJ1WhO/EKCiCJQcQFXHSUiInIYhnEO5uRqDn9WDXN1E7UQS0s1jNbtanao6Zbj0GhOCGvIHE6pRnPCFxI8zokiXP5U4Kvc8z/3nAD0n25Xa4iIiOh/GMY5XCRXrphVdeWUzqVciGV0NYwVoWYkH4dSnBLWRAK956Nw/9Nnz6FabBXDz2MnVaPZ/YUEj3OiCFdcEBjEAd6f0wazQo6IiMhmDOPIVkZXXTmtcykVYhldDeOkoaROCULDYVVYEwnbSo3e81F8f62P08MJ1WgCO89dJ4WSRGSSY/vkb2cYR0REZCuGcWQ7o6qunNK5VAtZzKiG0RJqmh3+OC0IDZUVYU2kbCsles9HqftreZxedlejiUmdu1YEtU4KJYlIghHzvDVsre92IiIisgzDOIoYTuhcap0LzoxqGKVQ0+zwxylBqBHMDmsiaVsp0Xs+yt1f7XF6OamS1L9NeuaTNILTQkki8mPUPG/JGd7HBjzXRFbFEREROQDDOIoYdnculUIWAAGVLlYuimBF+KMleHHLsEyzwxonhMZW0Hs+qp2nRp7HTl2UxMqg1opQ0i3nPJGjGD3PW//p3sdyNVUiIiJHYRjnIuzYKLO74kUuZJm7ai/W7Dni+1modLFqUQQrwh+1gMVtwzLNDGvsDo2tovd8lLq/lseF0z6nXUetDmrNPM7dds4TOYYZ87wlZzCEIyIichiGcS7Bjo02dla8yIUp/kEcYEyli55g1qrVVuWCF7cOyzQ6rPHfZ04bJmkWveej//1Pnz2HQ7/+AQDo07axFc21nR1BrRmhpFvPeSJH4DxvREREUYFhnAuwY6OPXRUvUoFUv3aNsPr7I0H3DafSRW8wa1XFoFzwEi3DMpVI7bOl43vYVulqZZWt3vNRuL//Nntu1b6o+ALC7upeo/CcJwoD53kjIiKKCgzjXIAdG294sHbPYQDeKhmnvm9xIAVAMowLtdIl1GBWa4VSuCGNVPCiVO0TDUOvlfbZ0C7JlrfHDVW24X4B4ebjyq7qXiO3WbQMxSYyDed5IyIiinhV7G4AqYv2js3MT3cjO28Dnlu1D8+t2ofsvA2Y+eluu5slKz21PoZ2SfYFU+N6twz4fTiVLkrBrJ52SRG2c8672w3dxnLbYOWuUlNez2nC2WdGkwu5CovKLG+LknC2mVnHcSgKi8qwZGux7u2rdq4azehtZvR1jyJfXl4eWrRogRo1aqBr165Yv3694v3XrVuHrl27okaNGmjZsiVefPHFgN/v2rULw4YNQ/PmzRETE4Pc3FwTW2+S5Ayg00gGcURERBGKlXEu0bdto4C5x8zu2DilskQqPADcNUzXyEoXs4JZs4dCS1UMZudtMOT1tByrdh7PTgrTrayyDWebh7rNnDSk3w0ViIB528ypK9aS8yxevBgTJkxAXl4eevbsiZdeeglZWVn47rvvkJqaGnT//fv34+qrr8bYsWPxxhtv4KuvvsL48ePRqFEjDBs2DADw+++/o2XLlrjhhhswceJEq98SERERkSqGcQ4n7tD1a9cI9/VrY2rHxkmdSKVKGDcN0zVqHjuz5pSyIqTx3wZLthYb8npajlW7j2cnzQMmF2YdOHYShUVlhrUp3G0e6jZzypB+J4WCaszcZk5csZacZ86cObjzzjsxZswYAEBubi5WrlyJ+fPnY8aMGUH3f/HFF5GamuqrdktLS0NBQQH+9a9/+cK4Sy+9FJdeeikAYPLkyda8kVAVF3A4KhERURRiGOdgUh261d8fwX392lj6mnZ2IpUqYaJlmK6YGRUnVldvGfF6Wo5VpxzPevaZmVV8UiEXAN8QcCOCSqO2eSjHuVOqEJ0SCmrhlG1G0enUqVPYsmVLUGA2YMAAbNiwQfIxGzduxIABAwJuGzhwIF555RWcPn0a1apVC6ktlZWVqKys9P1cUVER0vPokj9VtFDDBO98cURERBTxOGecg9kx15ST5rcCpOceAjj/kNFzShk9x5PaXFlGvJ6WY9VJx7OWfWbFfGeTs9KwdHwPPHBl66DfGTF/nJHbXO9x7pS5ytwUcElts37tGtnUmkChzrlH7nH06FGcPXsWiYmJAbcnJiaitLRU8jGlpaWS9z9z5gyOHj0acltmzJiB+Ph437+UlJSQn0uT4oLAIA7w/lxcYO7rEhERkSOwMs7BzO7QSVXgmDknmdYKF/F9hQoZN6ym6mZGVdxpHaIY7utpOVbdFIpYWcWXnlrftOotu7e5E+Yqc9LQZC2EbTZ31V6s2XMEq7/3/tNbKWlkVafdw8vJWjExMQE/ezyeoNvU7i91ux5TpkxBTk6O7+eKigpzA7lj++Rvj5bhqhyiS0REUYxhnIOZ2aGT6+iY8Zp6OlVK7XJqRzaShLud9QZK4byelmNVz/Fs96IlcuHYewUHAcDwNpkVmjkhiJI7rqzcx04IBfXyXyQI0BcGGxmeOWV4OZkvISEBsbGxQVVwhw8fDqp+EyQlJUnev2rVqmjYsGHIbYmLi0NcXFzIj9etYXB1suLtkYZDdImIKMoxjHM4Mzp0ah0dI19TT6fK6R0wu8MaN7B6riwtx6qW+zihCkcuBHtr00G8temg4W0yMzRzYhBlxz5205cI4Zy7Rl+73TTnHoWnevXq6Nq1K/Lz85Gdne27PT8/H9ddd53kYzIzM7Fs2bKA2z777DNkZGSEPF+cLZIzvAFUQCA1MToqxOSG6KYNjo73T0REBIZxrmB0h05LR8eo19TTqXJyB8wJYY0b2DFEUcuxqnQfp4TAcosrmNkmM0MzJwVRTtnHThbOuWv0tdvuoc5krZycHIwaNQoZGRnIzMzEggULUFRUhHHjxgHwDh/9+eef8frrrwMAxo0bh3nz5iEnJwdjx47Fxo0b8corr+Dtt9/2PeepU6fw3Xff+f7/559/xrZt21CnTh20bu2gyrP+070BVLQN1eQQXSIiIi7gEI2s7OjoeS2ndsDkOvKcVDyYUybQ18NJizwIiyvc1E16niIz2mT0YiBO5KR97FThnLtGX7vdeB2h0I0YMQK5ubl47LHH0LlzZ3zxxRdYvnw5mjVrBgAoKSlBUVGR7/4tWrTA8uXLsXbtWnTu3BmPP/445s6di2HDhvnuc+jQIaSnpyM9PR0lJSX417/+hfT0dIwZM8by96cqOQPoNDK6QqhoH6JLREQEVsZFJSvndNLzWk6Ya0qKkyv2nMiJQxSVOC0EFrbXW5sOBv3O7mDarZy2j50q1HPXjGu3264jFJ7x48dj/Pjxkr9buHBh0G29e/fG1q1bZZ+vefPmvkUdIkqkLHgQzUN0iYiI/ifGE5GfVsxXUVGB+Ph4lJeXo169enY3JyRWzoEWzmqqdissKkN23oag25eO7+GI9lH4xMOQ/9q7JSbZMAzZ/9hfuavU1jY57TwMl1P2cSSLtGPGLJHw+SEaOG4/ReKCB5ESLhIREf2Pns8PDONC5LgPaWSqSOnIs7Msz+5tIzUvoV2VQZE6R6Ld+5gI4OcHt3DUfiouAP59ZfDtY1YxxCIiInIQPZ8fOEyVSINIGDIVqQGLUexccEBpgYGhXZLDfm49x20kL3bgpEUliIg044IHREREEYdhXARgtYc13NyRj+SAJRKYNS9hKAEs50gkInIYLnhAREQUcRjGuRyrnUgLBizmCjcQN2OBgVADWC52QGZSOlf4xRKRDC54QEREFHEYxrkYq52ihxPDHvIyIhA3YzXKUANYp65qTO6ndK446YslhoLkSP2nA2mDueABERFRhGAY52KsdjKeEzthTg17yNhA3Oh5CcMJYCNhjkRyFqVzRfh/qd9Zfew5KRQkCpKcwRCOiIgoQjCMczFWOxnLiZ0wJ4c9ZHwgbuS8hOEGsG6eI5GcR+lcUXqMlccgq82JiIiIyCoM41yM1U7GcWonTK6junbPYdvDHnJ+IM4ANpgTq1+jQSjnitXnEavNiYiIiMgqDONcjp1tYzi1EybXGX1u1T5Unjlne+VetHNDIM4A9jwnVr9GC7VzRct5ZHaQ6vRwnYiIiIgiB8O4CMDOdvic2gmT6sAKnFC55wZmd+AZiLuDU6tftYqEir6B7ZMQV7UKAKBP28YB70PtPLIiSHVDuE5EREREkYFhHBGc3QmbnJWGuKpV8NyqfUG/s7tyz+msqoRiIO58ZlS/WhWQRUJFn/g9VJ45F7TN5M4jK4NUhutEREREZAWGcUT/4+ROWJ+2jSXDOLsr95zMbZVQkVD55GRGV79aFZC57TiWEu57sHoaAYbrRERERGS2KnY3gMhJ0lPrY2iXZMd1xITKPX9OqdxzqlBWb7TLzE93IztvA3Le3Y7svA2Y+eluu5tkmsKiMizZWozCojJLX9fIc0guXDLjPbnpOJYT7ntw6jQCREREREShYmUckUXCrXxycuWeE7mlAx8JlU9a2T3c0qhzyMpKLbccx0rCfQ9OnkaAiIiIiCgUUR3GZWdnY+3atbjyyivx/vvv290cimBGhRAcPqWdWzrwTl3J12hOCR2NOIesDMjcchwrMeI98MsIIiIiIookUR3G3X///bjjjjuwaNEiu5viGEbOW8U5sLycEkJEIzd04COh8kmLSAodrQ7I3HAcqzHiPfDLCCIiIiKKFFEdxvXt2xdr1661uxmOYeQQMvFzZac3Ra82jUzrSDo5+NMaQjj5PbiZ3g681fshEiqftIi00NHqgCwSgqhIeA9EREREREZwZRj3xRdf4Omnn8aWLVtQUlKCpUuX4vrrrw+6X15eHp5++mmUlJSgffv2yM3NRa9evaxvsAsYWb0l9VxLCw9haeEhAMbPE2X3PFRqtIQQTn8P0cKu/RAJlU9qIjF0ZLhEREREREShcOVqqidPnkSnTp0wb9482fssXrwYEyZMwMMPP4zCwkL06tULWVlZKCoqsrCl7mHkin1qjzFy1UErVzUMldoqjm54D9HA7v3g1JV8jTQ5Kw1Lx/fAnBs7Yen4HpjEwJmIiIiIiKKQKyvjsrKykJWVpXifOXPm4M4778SYMWMAALm5uVi5ciXmz5+PGTNm6H7NyspKVFZW+n6uqKjQ/RxOZuQQMi2PMWqeKLfMQ6VU+eSW9xDpuB+swWoyIiIiIiKKdq6sjFNz6tQpbNmyBQMGDAi4fcCAAdiwYUNIzzljxgzEx8f7/qWkpBjRVMdQq94K97nEjJonyk3zUMlVPrnpPUQyue194NhJVikSERERERGRYSIyjDt69CjOnj2LxMTEgNsTExN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" ] @@ -476,39 +476,39 @@ "fig, axes = plt.subplots(1, 2, figsize=(15, 6))\n", "\n", "def scattered_mean(distribution, burn_in, n, jump, ax, title, color, ylog=False):\n", - " \n", - " #Set a jump to reduce simulation complexity\n", - " sample_means = [np.mean(distribution.rvs(size=i)) \n", - " for i in range(burn_in, n+1, jump)]\n", - " \n", - " ax.scatter(range(burn_in, n+1, jump), sample_means, s=10, c=color)\n", - " \n", - " #Change the y-axis to log scale if necessory\n", - " if ylog:\n", - " ax.set_yscale(\"symlog\")\n", - " ax.set_title(title, size=10)\n", - " ax.set_xlabel(r\"$n$\", size=12)\n", - " ax.set_ylabel(r\"$\\bar x$\", size=12)\n", - " yabs_max = max(ax.get_ylim(), key=abs)\n", - " ax.set_ylim(ymin=-yabs_max, ymax=yabs_max)\n", - " return ax\n", + " \n", + " #Set a jump to reduce simulation complexity\n", + " sample_means = [np.mean(distribution.rvs(size=i)) \n", + " for i in range(burn_in, n+1, jump)]\n", + " \n", + " ax.scatter(range(burn_in, n+1, jump), sample_means, s=10, c=color)\n", + " \n", + " #Change the y-axis to log scale if necessory\n", + " if ylog:\n", + " ax.set_yscale(\"symlog\")\n", + " ax.set_title(title, size=10)\n", + " ax.set_xlabel(r\"$n$\", size=12)\n", + " ax.set_ylabel(r\"$\\bar x$\", size=12)\n", + " yabs_max = max(ax.get_ylim(), key=abs)\n", + " ax.set_ylim(ymin=-yabs_max, ymax=yabs_max)\n", + " return ax\n", "\n", "scattered_mean(distribution=st.cauchy(), \n", - " burn_in=1000, \n", - " n=1_000_000, \n", - " ax=axes[0],\n", - " jump=2000,\n", - " title=\"Cauchy Distribution\",\n", - " color='#1f77b4',\n", - " ylog=True)\n", + " burn_in=1000, \n", + " n=1_000_000, \n", + " ax=axes[0],\n", + " jump=2000,\n", + " title=\"Cauchy Distribution\",\n", + " color='#1f77b4',\n", + " ylog=True)\n", "\n", "scattered_mean(distribution=st.norm(), \n", - " burn_in=1000, \n", - " n=1_000_000,\n", - " ax=axes[1],\n", - " jump=2000,\n", - " title=\"Normal Distribution\",\n", - " color='#ff7f0e')\n", + " burn_in=1000, \n", + " n=1_000_000,\n", + " ax=axes[1],\n", + " jump=2000,\n", + " title=\"Normal Distribution\",\n", + " color='#ff7f0e')\n", "\n", "fig.suptitle('Sample Mean with Different Sample Size')\n", "plt.show()" @@ -516,17 +516,17 @@ }, { "cell_type": "markdown", - "id": "4e126f26-eb95-4c3c-b579-00edb27c826a", + "id": "8b791a86", "metadata": {}, "source": [ - "We can see that unlike normal distribution, Cauchy distribution does not have a convergence that LLN implies.\n", + "We can see that unlike normal distribution, Cauchy distribution does not have the convergence that LLN implies.\n", "\n", "It is also not hard to conjecture that LLN can be broken when the IID assumption is violated." ] }, { "cell_type": "markdown", - "id": "d9f61c65-b2d8-4989-95dd-0837b635e9ff", + "id": "8a9f6739", "metadata": {}, "source": [ "Let's go through a very simple example where LLN fails with IID violated:\n", @@ -546,10 +546,10 @@ "We can then see that \n", "\n", "$$\n", - "\\bar X_n := \\frac{1}{n} \\sum_{t=1}^n X_i = X_1 \\sim \\mathcal{N}(0,1)\n", + "\\bar X_n := \\frac{1}{n} \\sum_{t=1}^n X_i = X_1 \\sim \\mathcal{N}(0,1)\n", "$$\n", "\n", - "Therefore, the distribution of mean of X follows $\\mathcal{N}(0,1)$.\n", + "Therefore, the distribution of the mean of X follows $\\mathcal{N}(0,1)$.\n", "\n", "However,\n", "\n", @@ -566,7 +566,7 @@ }, { "cell_type": "markdown", - "id": "59934170", + "id": "73902f5a", "metadata": {}, "source": [ "## CLT\n", @@ -610,7 +610,7 @@ }, { "cell_type": "markdown", - "id": "928cdff7", + "id": "5b7ca292", "metadata": { "tags": [] }, @@ -637,12 +637,12 @@ { "cell_type": "code", "execution_count": 10, - "id": "c6444237", + "id": "dc6bf8f3", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] @@ -653,9 +653,9 @@ ], "source": [ "# Set parameters\n", - "n = 250 # Choice of n\n", - "k = 1_000_000 # Number of draws of Y_n\n", - "distribution = st.expon(2) # Exponential distribution, λ = 1/2\n", + "n = 250 # Choice of n\n", + "k = 1_000_000 # Number of draws of Y_n\n", + "distribution = st.expon(2) # Exponential distribution, λ = 1/2\n", "μ, σ = distribution.mean(), distribution.std()\n", "\n", "# Draw underlying RVs. Each row contains a draw of X_1,..,X_n\n", @@ -679,7 +679,7 @@ }, { "cell_type": "markdown", - "id": "48f02fa4", + "id": "0e81bddf", "metadata": {}, "source": [ "(Notice the absence of for loops --- every operation is vectorized, meaning that the major calculations are all shifted to optimized C code.)\n", @@ -689,7 +689,7 @@ }, { "cell_type": "markdown", - "id": "7229ffd3", + "id": "34a77889", "metadata": {}, "source": [ "## Exercises" @@ -697,7 +697,7 @@ }, { "cell_type": "markdown", - "id": "89258210-db73-4470-85a7-033b21a072b1", + "id": "f80f94a3", "metadata": {}, "source": [ "## Ex 1" @@ -705,15 +705,15 @@ }, { "cell_type": "markdown", - "id": "40206358-6c49-4a4c-9c81-a6ae70d9c8fe", + "id": "b9537695", "metadata": {}, "source": [ - "Repeat the simulation in (TODO: Add a reference to simulation one) with [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution). " + "Repeat the simulation in (TODO: Add a reference to simulation one) with [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution)." ] }, { "cell_type": "markdown", - "id": "f65d6d4a-4aa4-4ce1-b047-21b8eb682cd9", + "id": "2db66fc9", "metadata": {}, "source": [ "Solution:" @@ -722,12 +722,12 @@ { "cell_type": "code", "execution_count": 11, - "id": "95967ca5-c970-4236-b8e4-6296989dc81f", + "id": "8c3c06ab", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] @@ -738,9 +738,9 @@ ], "source": [ "# Set parameters\n", - "n = 250 # Choice of n\n", - "k = 1_000_000 # Number of draws of Y_n\n", - "distribution = st.beta(2,2) # Exponential distribution, λ = 1/2\n", + "n = 250 # Choice of n\n", + "k = 1_000_000 # Number of draws of Y_n\n", + "distribution = st.beta(2,2) # Exponential distribution, λ = 1/2\n", "μ, σ = distribution.mean(), distribution.std()\n", "\n", "# Draw underlying RVs. Each row contains a draw of X_1,..,X_n\n", @@ -764,7 +764,7 @@ }, { "cell_type": "markdown", - "id": "b49befe8", + "id": "dc5410ce", "metadata": {}, "source": [ "## Ex 2" @@ -772,7 +772,7 @@ }, { "cell_type": "markdown", - "id": "2ed84c17", + "id": "ba22dc50", "metadata": {}, "source": [ "Although NumPy doesn't give us a `bernoulli` function, we can generate a draw of $X$ using NumPy via" @@ -781,7 +781,7 @@ { "cell_type": "code", "execution_count": 12, - "id": "1b300696", + "id": "904b490a", "metadata": {}, "outputs": [ { @@ -800,7 +800,7 @@ }, { "cell_type": "markdown", - "id": "dcd111f0", + "id": "d10e3d75", "metadata": {}, "source": [ "Explain why this provides a random variable $X$ with the right distribution." @@ -808,7 +808,7 @@ }, { "cell_type": "markdown", - "id": "c7564cf9", + "id": "fd00362c", "metadata": {}, "source": [ "Solution:" @@ -816,7 +816,7 @@ }, { "cell_type": "markdown", - "id": "2fa6cb25", + "id": "c9dc395c", "metadata": {}, "source": [ "We can write $X$ as $X = \\mathbf 1\\{U < p\\}$ where $\\mathbf 1$ is the [indicator function](https://en.wikipedia.org/wiki/Indicator_function) (i.e., 1 if the statement is true and zero otherwise).\n", @@ -832,7 +832,7 @@ }, { "cell_type": "markdown", - "id": "c03dd62e-994e-4976-8e6e-bcb196da9013", + "id": "53659cd9", "metadata": {}, "source": [ "## Ex 3" @@ -840,7 +840,7 @@ }, { "cell_type": "markdown", - "id": "79776f08-aeda-4642-bdfe-1931548e1f3f", + "id": "fe57b8aa", "metadata": {}, "source": [ "We mentioned above that it is possible for LLN to hold when IID is violated.\n", @@ -848,27 +848,33 @@ "Let's investigate this claim further.\n", "\n", "Assume we have a AR(1) process as below:\n", - "\n", "$$\n", - "X_{t+1} = \\alpha + \\beta X_t + \\sigma \\epsilon _{t+1}\n", + "X_{t+1} = \\alpha + \\beta X_t + \\sigma \\epsilon _{t+1}\n", "$$\n", "\n", "$$\n", - "X_0 \\sim \\mathcal{N}(\\frac{\\alpha}{1-\\beta}, \\frac{\\alpha^2}{1-\\beta^2})\n", + "X_0 \\sim \\mathcal{N} \\left(\\frac{\\alpha}{1-\\beta}, \\frac{\\sigma^2}{1-\\beta^2}\\right)\n", "$$\n", "\n", "where $\\epsilon_t \\sim \\mathcal{N}(0,1)$\n", "\n", - "Show LLN holds using simulations with $\\alpha = 0.8$, $\\beta = 0.2$." + "1. Prove this process violated the independence assumption but not the identically distributed assumption;\n", + "2. Show LLN holds using simulations with $\\alpha = 0.8$, $\\beta = 0.2$." ] }, { "cell_type": "markdown", - "id": "694d0c2e-dd9b-402b-a4f6-ff576cf15b1f", + "id": "fb921dc0", "metadata": {}, "source": [ "Solution:\n", "\n", + "1. \n", + "\n", + "Given X_{t+1} is dependent on X_t, this process is not independent.\n", + "\n", + "To check whether it is identically distributed, we need to check whether the distribution in $T={0...n}$\n", + "\n", "Let's verify the expectation and variance of this AR(1) process using pen and paper first.\n", "\n", "$$\n", @@ -882,89 +888,39 @@ "\n", "$$\n", "\\begin{aligned}\n", - "\\mathbb Var X_t &= \\beta^2 \\mathbb Var X_{t-1} + \\sigma^2\\\\\n", + "Var(X_t+1) &= \\beta^2 Var(X_{t}) + \\sigma^2\\\\\n", + "&= \\frac{\\beta^2\\sigma^2}{1-\\beta^2} + \\sigma^2 \\\\\n", + "&= \\frac{\\sigma^2}{1-\\beta^2}\n", "\\end{aligned}\n", "$$ \n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "deccd68a-e528-4be3-bf0c-14b1581680c7", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Simulated Variance is 104.16666666666667\n" - ] - } - ], - "source": [ - "import scipy.stats as st\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", "\n", - "σ = 10\n", - "α = 0.8\n", - "β = 0.2\n", - "n = 100_000\n", + "We find that expectation and variance are the same $t = 0, ..., n$.\n", "\n", - "var = np.ones(n)\n", - "var[0] = α**2/(1-β**2)\n", - "for t in range(n-1):\n", - " var[t+1] = β**2*var[t]+σ**2\n", - "plt.plot(var)\n", - "plt.show()\n", + "Given both $X_0$ and $\\epsilon _{0}$ are normally distributed and independent from each other, the weighted sum of the two normally distributed random variables is also normally distributed.\n", "\n", - "print(f'Simulated Variance is {var[-1]}')" - ] - }, - { - "cell_type": "markdown", - "id": "62e5c20e-1644-45ae-b178-a883b726a198", - "metadata": {}, - "source": [ - "Note that\n", + "This holds true for all $X_t$ and $\\epsilon _{t}$ where $t = 0, ..., n$\n", + "\n", + "Therefore, \n", "\n", "$$\n", - "\\begin{aligned}\n", - "\\mathbb Var X_t &= \\beta^2 \\mathbb Var X_{t-1} + \\sigma^2\\\\\n", - "\\end{aligned}\n", + "X_t \\sim \\mathcal{N} \\left(\\frac{\\alpha}{1-\\beta}, \\frac{\\sigma^2}{1-\\beta^2}\\right) \\quad t = 0, ..., n\n", "$$ \n", "\n", - "has a stable fixed point.\n", "\n", + "We can conclude this AR(1) process violates the independence assumption but is identically distributed.\n", "\n", - "Thus, assuming $\\mathbb Var X_t^* = X_{t-1}^*$, we have\n", - "$$\n", - "\\begin{aligned}\n", - "\\mathbb Var X_t &= \\frac{\\sigma^2}{1-\\beta^2}\\\\\n", - "\\end{aligned}\n", - "$$" + "2." ] }, { "cell_type": "code", - "execution_count": 22, - "id": "622c8cdb-e830-4ef3-9b1a-a273b589d79c", + "execution_count": 19, + "id": "4bcd7f2d", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -974,17 +930,22 @@ } ], "source": [ + "σ = 10\n", + "α = 0.8\n", + "β = 0.2\n", + "n = 100_000\n", + "\n", "fig, ax = plt.subplots(figsize=(10, 6))\n", "x = np.ones(n)\n", "x[0] = st.norm.rvs(α/(1-β), α**2/(1-β**2))\n", "ϵ = st.norm.rvs(size=n+1)\n", "means = np.ones(n)\n", "for t in range(n-1):\n", - " x[t+1] = α + β * x[t] + σ * ϵ[t+1]\n", - " means[t+1] = np.mean(x[:t])\n", + " x[t+1] = α + β * x[t] + σ * ϵ[t+1]\n", + " means[t+1] = np.mean(x[:t+1])\n", "\n", "\n", - "ax.scatter(range(n), means, s=10, alpha=0.5)\n", + "ax.scatter(range(100, n), means[100:n], s=10, alpha=0.5)\n", "\n", "ax.set_xlabel(r\"$n$\", size=12)\n", "ax.set_ylabel(r\"$\\bar x$\", size=12)\n", @@ -997,7 +958,7 @@ }, { "cell_type": "markdown", - "id": "00e14b9a", + "id": "a3111332", "metadata": {}, "source": [ "```{solution-end}\n", @@ -1006,10 +967,10 @@ }, { "cell_type": "markdown", - "id": "d40afcf5-6106-4b82-bfd9-7efce3cee066", + "id": "96f9e087", "metadata": {}, "source": [ - "We see the convergence in $\\bar x$ to $\\mu$ even when IID assumption is violated." + "We see the convergence of $\\bar x$ around $\\mu$ even when the independence assumption is violated." ] } ], diff --git a/in-work/lln_clt.md b/in-work/lln_clt.md index 3ea4e4902..88cf01eab 100644 --- a/in-work/lln_clt.md +++ b/in-work/lln_clt.md @@ -90,7 +90,7 @@ Let's check this: ```{code-cell} ipython3 n = 1_000_000 X_draws = st.bernoulli.rvs(p, size=n) -print(X_draws.mean()) # count the number of 1's and divide by n +print(X_draws.mean()) # count the number of 1's and divide by n ``` If we change $p$ the claim still holds: @@ -135,13 +135,13 @@ The traditional version of the law of large numbers concerns independent and ide Let $X_1, \ldots, X_n$ be independent and identically distributed random variables. -This random variables can be continuous or discrete. +These random variables can be continuous or discrete. For simplicity we will assume they are continuous and we let $f$ denote their density function, so that, for any $i$ in $\{1, \ldots, n\}$ $$ - \mathbb P\{a \leq X_i \leq b\} = \int_a^b f(x) dx + \mathbb P\{a \leq X_i \leq b\} = \int_a^b f(x) dx $$ (For the discrete case, we need to replace densities with probability mass functions and integrals with sums.) @@ -149,7 +149,7 @@ $$ Let $\mu$ denote the common mean of this sample: $$ - \mu := \mathbb E X = \int_{-\infty}^{\infty} x f(dx) + \mu := \mathbb E X = \int_{-\infty}^{\infty} x f(dx) $$ In addition, let @@ -217,31 +217,31 @@ Let's run some simulations to visualize LLN ```{code-cell} ipython3 def generate_histogram(X_distribution, n, m): - fig, ax = plt.subplots(figsize=(10, 6)) - - def draw_means(X_distribution, n): - - # Step 3: Generate n draws: X_1, ..., X_n - X_samples = X_distribution.rvs(size=n) - - # Step 4: Calculate sample mean - return np.mean(X_samples) - - # Step 5: Loop m times - sample_means = [draw_means(X_distribution, n) for i in range(m)] - print(f'The mean of sample mean is {round(np.mean(sample_means),2)}') - - # Generate a histogram - ax.hist(sample_means, bins=30, alpha=0.5, density=True) - mu = X_distribution.mean() - if not np.isnan(mu): - ax.axvline(x=mu, ls="--", lw=3, label=fr"$\mu = {mu}$") - - ax.set_xlim(min(sample_means), max(sample_means)) - ax.set_xlabel(r'$\bar x$') - ax.set_ylabel('Density') - ax.legend() - plt.show() + fig, ax = plt.subplots(figsize=(10, 6)) + + def draw_means(X_distribution, n): + + # Step 3: Generate n draws: X_1, ..., X_n + X_samples = X_distribution.rvs(size=n) + + # Step 4: Calculate the sample mean + return np.mean(X_samples) + + # Step 5: Loop m times + sample_means = [draw_means(X_distribution, n) for i in range(m)] + print(f'The mean of sample mean is {round(np.mean(sample_means),2)}') + + # Generate a histogram + ax.hist(sample_means, bins=30, alpha=0.5, density=True) + mu = X_distribution.mean() + if not np.isnan(mu): + ax.axvline(x=mu, ls="--", lw=3, label=fr"$\mu = {mu}$") + + ax.set_xlim(min(sample_means), max(sample_means)) + ax.set_xlabel(r'$\bar x$') + ax.set_ylabel('Density') + ax.legend() + plt.show() ``` ```{code-cell} ipython3 @@ -252,39 +252,39 @@ generate_histogram(st.norm(loc=5, scale=2), n=50_000, m=1000) We can see that the distribution of $\bar X$ is clustered around $\mathbb E X$ as expected. -We can increase values for `n` and `m` to see how the distribution changes by slightly changing the code to see the changes with an increasing $n$ +We can vary values for `n` to see how the distribution changes ```{code-cell} ipython3 def generate_multiple_hist(X_distribution, ns, m, log_scale=False): - _, ax = plt.subplots(figsize=(10, 6)) - - def draw_means(X_distribution, n): - X_samples = X_distribution.rvs(size=n) - return np.mean(X_samples) - - for n in ns: - sample_means = [draw_means(X_distribution, n) for i in range(m)] - if log_scale: - plt.xscale('symlog') - ax.hist(sample_means, bins=60, alpha=0.4, density=True, label=fr'$n = {n}$') - - mu = X_distribution.mean() - if not np.isnan(mu): - ax.axvline(x=mu, ls="--", lw=3, label=fr"$\mu = {mu}$") - - ax.set_xlim(min(sample_means), max(sample_means)) - ax.set_xlabel(r'$\bar x$') - ax.set_ylabel('Density') - ax.set(title=fr'$n = {n}, m = {m}$') - ax.legend() - plt.show() + _, ax = plt.subplots(figsize=(10, 6)) + + def draw_means(X_distribution, n): + X_samples = X_distribution.rvs(size=n) + return np.mean(X_samples) + + for n in ns: + sample_means = [draw_means(X_distribution, n) for i in range(m)] + if log_scale: + plt.xscale('symlog') + ax.hist(sample_means, bins=60, alpha=0.4, density=True, label=fr'$n = {n}$') + + mu = X_distribution.mean() + if not np.isnan(mu): + ax.axvline(x=mu, ls="--", lw=3, label=fr"$\mu = {mu}$") + + ax.set_xlim(min(sample_means), max(sample_means)) + ax.set_xlabel(r'$\bar x$') + ax.set_ylabel('Density') + ax.set(title=fr'$n = {n}, m = {m}$') + ax.legend() + plt.show() ``` ```{code-cell} ipython3 generate_multiple_hist(st.norm(loc=5, scale=2), ns=[20_000, 50_000, 100_000], m=10_000) ``` -We see that the histogram gradually converge to $\mu$. +We see that the histogram gradually converges to $\mu$. You can imagine the result when extrapolating this trend for $n \to \infty$. @@ -300,51 +300,51 @@ We can demonstrate this using a simple simulation using a [Cauchy distribution]( +++ -We lost the convergence we have seen before with normal distribution +We lost the convergence we have seen before with normal distribution ```{code-cell} ipython3 fig, axes = plt.subplots(1, 2, figsize=(15, 6)) def scattered_mean(distribution, burn_in, n, jump, ax, title, color, ylog=False): - - #Set a jump to reduce simulation complexity - sample_means = [np.mean(distribution.rvs(size=i)) - for i in range(burn_in, n+1, jump)] - - ax.scatter(range(burn_in, n+1, jump), sample_means, s=10, c=color) - - #Change the y-axis to log scale if necessory - if ylog: - ax.set_yscale("symlog") - ax.set_title(title, size=10) - ax.set_xlabel(r"$n$", size=12) - ax.set_ylabel(r"$\bar x$", size=12) - yabs_max = max(ax.get_ylim(), key=abs) - ax.set_ylim(ymin=-yabs_max, ymax=yabs_max) - return ax + + #Set a jump to reduce simulation complexity + sample_means = [np.mean(distribution.rvs(size=i)) + for i in range(burn_in, n+1, jump)] + + ax.scatter(range(burn_in, n+1, jump), sample_means, s=10, c=color) + + #Change the y-axis to log scale if necessory + if ylog: + ax.set_yscale("symlog") + ax.set_title(title, size=10) + ax.set_xlabel(r"$n$", size=12) + ax.set_ylabel(r"$\bar x$", size=12) + yabs_max = max(ax.get_ylim(), key=abs) + ax.set_ylim(ymin=-yabs_max, ymax=yabs_max) + return ax scattered_mean(distribution=st.cauchy(), - burn_in=1000, - n=1_000_000, - ax=axes[0], - jump=2000, - title="Cauchy Distribution", - color='#1f77b4', - ylog=True) + burn_in=1000, + n=1_000_000, + ax=axes[0], + jump=2000, + title="Cauchy Distribution", + color='#1f77b4', + ylog=True) scattered_mean(distribution=st.norm(), - burn_in=1000, - n=1_000_000, - ax=axes[1], - jump=2000, - title="Normal Distribution", - color='#ff7f0e') + burn_in=1000, + n=1_000_000, + ax=axes[1], + jump=2000, + title="Normal Distribution", + color='#ff7f0e') fig.suptitle('Sample Mean with Different Sample Size') plt.show() ``` -We can see that unlike normal distribution, Cauchy distribution does not have a convergence that LLN implies. +We can see that unlike normal distribution, Cauchy distribution does not have the convergence that LLN implies. It is also not hard to conjecture that LLN can be broken when the IID assumption is violated. @@ -367,10 +367,10 @@ $$ We can then see that $$ -\bar X_n := \frac{1}{n} \sum_{t=1}^n X_i = X_1 \sim \mathcal{N}(0,1) +\bar X_n := \frac{1}{n} \sum_{t=1}^n X_i = X_1 \sim \mathcal{N}(0,1) $$ -Therefore, the distribution of mean of X follows $\mathcal{N}(0,1)$. +Therefore, the distribution of the mean of X follows $\mathcal{N}(0,1)$. However, @@ -381,7 +381,7 @@ $$ which violates {eq}`exp`, and thus breaks LLN. ```{note} -Although in this case, the violation of IID breaks LLN, it is not always the case for correlated data (TODO: Link to MC Lecture) +Although in this case, the violation of IID breaks LLN, it is not always the case for correlated data (TODO: Link to Exercise) ``` +++ @@ -446,9 +446,9 @@ $F(x) = 1 - e^{- \lambda x}$. ```{code-cell} ipython3 # Set parameters -n = 250 # Choice of n -k = 1_000_000 # Number of draws of Y_n -distribution = st.expon(2) # Exponential distribution, λ = 1/2 +n = 250 # Choice of n +k = 1_000_000 # Number of draws of Y_n +distribution = st.expon(2) # Exponential distribution, λ = 1/2 μ, σ = distribution.mean(), distribution.std() # Draw underlying RVs. Each row contains a draw of X_1,..,X_n @@ -484,7 +484,7 @@ The fit to the normal density is already tight and can be further improved by in +++ -Repeat the simulation in (TODO: Add a reference) with [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution). +Repeat the simulation in (TODO: Add a reference to simulation one) with [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution). +++ @@ -492,9 +492,9 @@ Solution: ```{code-cell} ipython3 # Set parameters -n = 250 # Choice of n -k = 1_000_000 # Number of draws of Y_n -distribution = st.beta(2,2) # Exponential distribution, λ = 1/2 +n = 250 # Choice of n +k = 1_000_000 # Number of draws of Y_n +distribution = st.beta(2,2) # Exponential distribution, λ = 1/2 μ, σ = distribution.mean(), distribution.std() # Draw underlying RVs. Each row contains a draw of X_1,..,X_n @@ -548,5 +548,104 @@ This means that $X = \mathbf 1\{U < p\}$ has the right distribution. +++ +## Ex 3 + ++++ + +We mentioned above that it is possible for LLN to hold when IID is violated. + +Let's investigate this claim further. + +Assume we have a AR(1) process as below: +$$ +X_{t+1} = \alpha + \beta X_t + \sigma \epsilon _{t+1} +$$ + +$$ +X_0 \sim \mathcal{N} \left(\frac{\alpha}{1-\beta}, \frac{\sigma^2}{1-\beta^2}\right) +$$ + +where $\epsilon_t \sim \mathcal{N}(0,1)$ + +1. Prove this process violated the independence assumption but not the identically distributed assumption; +2. Show LLN holds using simulations with $\alpha = 0.8$, $\beta = 0.2$. + ++++ + +Solution: + +1. + +Given X_{t+1} is dependent on X_t, this process is not independent. + +To check whether it is identically distributed, we need to check whether the distribution in $T={0...n}$ + +Let's verify the expectation and variance of this AR(1) process using pen and paper first. + +$$ +\begin{aligned} +\mathbb E X_{t+1} &= \alpha + \beta \mathbb E X_t \\ +&= \alpha + \beta \frac{\alpha}{1-\beta} \\ +&= \frac{\alpha}{1-\beta} +\end{aligned} +$$ + + +$$ +\begin{aligned} +Var(X_t+1) &= \beta^2 Var(X_{t}) + \sigma^2\\ +&= \frac{\beta^2\sigma^2}{1-\beta^2} + \sigma^2 \\ +&= \frac{\sigma^2}{1-\beta^2} +\end{aligned} +$$ + +We find that expectation and variance are the same $t = 0, ..., n$. + +Given both $X_0$ and $\epsilon _{0}$ are normally distributed and independent from each other, the weighted sum of the two normally distributed random variables is also normally distributed. + +This holds true for all $X_t$ and $\epsilon _{t}$ where $t = 0, ..., n$ + +Therefore, + +$$ +X_t \sim \mathcal{N} \left(\frac{\alpha}{1-\beta}, \frac{\sigma^2}{1-\beta^2}\right) \quad t = 0, ..., n +$$ + + +We can conclude this AR(1) process violates the independence assumption but is identically distributed. + +2. + +```{code-cell} ipython3 +σ = 10 +α = 0.8 +β = 0.2 +n = 100_000 + +fig, ax = plt.subplots(figsize=(10, 6)) +x = np.ones(n) +x[0] = st.norm.rvs(α/(1-β), α**2/(1-β**2)) +ϵ = st.norm.rvs(size=n+1) +means = np.ones(n) +for t in range(n-1): + x[t+1] = α + β * x[t] + σ * ϵ[t+1] + means[t+1] = np.mean(x[:t+1]) + + +ax.scatter(range(100, n), means[100:n], s=10, alpha=0.5) + +ax.set_xlabel(r"$n$", size=12) +ax.set_ylabel(r"$\bar x$", size=12) +yabs_max = max(ax.get_ylim(), key=abs) +ax.axhline(y=α/(1-β), ls="--", lw=3, label=r"$\mu = \frac{\alpha}{1-\beta}$",color = 'black') + +plt.legend() +plt.show() +``` + ```{solution-end} ``` + ++++ + +We see the convergence of $\bar x$ around $\mu$ even when the independence assumption is violated. From b3d8b96bf0cd1895a43278082a8ba79d6f9344d7 Mon Sep 17 00:00:00 2001 From: Humphrey Yang Date: Fri, 3 Feb 2023 13:19:58 +1100 Subject: [PATCH 09/12] update --- in-work/lln_clt.ipynb | 998 ------------------------------------------ in-work/lln_clt.md | 70 +-- 2 files changed, 35 insertions(+), 1033 deletions(-) delete mode 100644 in-work/lln_clt.ipynb diff --git a/in-work/lln_clt.ipynb b/in-work/lln_clt.ipynb deleted file mode 100644 index 44e60072e..000000000 --- a/in-work/lln_clt.ipynb +++ /dev/null @@ -1,998 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "7d6e1b22", - "metadata": {}, - "source": [ - "## LLN and CLT\n", - "\n", - "## Overview\n", - "\n", - "This lecture illustrates two of the most important theorems of probability and statistics: The\n", - "law of large numbers (LLN) and the central limit theorem (CLT).\n", - "\n", - "These beautiful theorems lie behind many of the most fundamental results in econometrics and quantitative economic modeling.\n", - "\n", - "The lecture is based around simulations that show the LLN and CLT in action.\n", - "\n", - "We also demonstrate how the LLN and CLT break down when the assumptions they are based on do not hold.\n", - "\n", - "In addition, we examine several useful extensions of the classical theorems, such as\n", - "\n", - "* The delta method, for smooth functions of random variables, and\n", - "* the multivariate case.\n", - "\n", - "Some of these extensions are presented as exercises.\n", - "\n", - "We'll need the following imports:" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "a8a9c791", - "metadata": {}, - "outputs": [], - "source": [ - "import matplotlib.pyplot as plt\n", - "import random\n", - "import numpy as np\n", - "import scipy.stats as st" - ] - }, - { - "cell_type": "markdown", - "id": "27b198f3", - "metadata": {}, - "source": [ - "## Relationships\n", - "\n", - "\n", - "The LLN gives conditions under which sample moments converge to population moments as sample size increases.\n", - "\n", - "The CLT provides information about the rate at which sample moments converge to population moments as sample size increases.\n", - "\n", - "(lln_mr)=\n", - "## LLN\n", - "\n", - "```{index} single: Law of Large Numbers\n", - "```\n", - "\n", - "We begin with the law of large numbers, which tells us when sample averages\n", - "will converge to their population means.\n", - "\n", - "### The LLN in Action\n", - "\n", - "Let's see an example of the LLN in action before we go further.\n", - "\n", - "Consider a [Bernoulli random variable](https://en.wikipedia.org/wiki/Bernoulli_distribution) $X$ with parameter $p$.\n", - "\n", - "This means that $X$ takes values in $\\{0,1\\}$ and $\\mathbb P\\{X=1\\} = p$.\n", - "\n", - "We can think of drawing $X$ as tossing a biased coin where\n", - "\n", - "* the coin falls on \"heads\" with probability $p$ and\n", - "* we set $X=1$ if the coin is \"heads\" and zero otherwise.\n", - "\n", - "The mean of $X$ is \n", - "\n", - "$$\n", - "\\mathbb E X = 0 \\cdot \\mathbb P\\{X=0\\} + 1 \\cdot \\mathbb P\\{X=1\\} = \\mathbb P\\{X=1\\} = p\n", - "$$\n", - "\n", - "We can generate a draw of $X$ with `scipy.stats` (imported as `st`) as follows:" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "e908d632", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0\n" - ] - } - ], - "source": [ - "p = 0.8\n", - "X = st.bernoulli.rvs(p)\n", - "print(X)" - ] - }, - { - "cell_type": "markdown", - "id": "5458e7ef", - "metadata": {}, - "source": [ - "In this setting, the LLN tells us if we flip the coin many times, the fraction of heads that we see will be close to $p$.\n", - "\n", - "Let's check this:" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "9815c7fc", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.799818\n" - ] - } - ], - "source": [ - "n = 1_000_000\n", - "X_draws = st.bernoulli.rvs(p, size=n)\n", - "print(X_draws.mean()) # count the number of 1's and divide by n" - ] - }, - { - "cell_type": "markdown", - "id": "eb4e5a32", - "metadata": {}, - "source": [ - "If we change $p$ the claim still holds:" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "9810b20f", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.299727\n" - ] - } - ], - "source": [ - "p = 0.3\n", - "X_draws = st.bernoulli.rvs(p, size=n)\n", - "print(X_draws.mean())" - ] - }, - { - "cell_type": "markdown", - "id": "70bcf799", - "metadata": {}, - "source": [ - "Let's connect this to the discussion above, where we said the sample average converges to the \"population mean\".\n", - "\n", - "The population mean is the mean in an infinite sample, which equals the true mean, or $\\mathbb E X$.\n", - "\n", - "The sample mean of the draws $X_1, \\ldots, X_n$ is\n", - "\n", - "$$\n", - "\\bar X_n := \\frac{1}{n} \\sum_{i=1}^n X_i\n", - "$$\n", - "\n", - "which, in this case, is the fraction of draws that equal one (the number of heads divided by $n$).\n", - "\n", - "Thus, the LLN tells us that\n", - "\n", - "```{math}\n", - ":label: exp\n", - "\n", - "\\bar X_n \\to \\mathbb E X = p\n", - "\\qquad (n \\to \\infty)\n", - "```\n", - "\n", - "This is exactly what we illustrated in the code above." - ] - }, - { - "cell_type": "markdown", - "id": "76ab8554", - "metadata": { - "jp-MarkdownHeadingCollapsed": true, - "tags": [] - }, - "source": [ - "(lln_ksl)=\n", - "### Statement of the LLN\n", - "\n", - "Let's state the LLN more carefully.\n", - "\n", - "The traditional version of the law of large numbers concerns independent and identically distributed (IID) random variables.\n", - "\n", - "Let $X_1, \\ldots, X_n$ be independent and identically distributed random variables.\n", - "\n", - "These random variables can be continuous or discrete.\n", - "\n", - "For simplicity we will assume they are continuous and we let $f$ denote their density function, so that, for any $i$ in $\\{1, \\ldots, n\\}$\n", - "\n", - "\n", - "$$ \n", - " \\mathbb P\\{a \\leq X_i \\leq b\\} = \\int_a^b f(x) dx\n", - "$$\n", - "\n", - "(For the discrete case, we need to replace densities with probability mass functions and integrals with sums.)\n", - "\n", - "Let $\\mu$ denote the common mean of this sample:\n", - "\n", - "$$\n", - " \\mu := \\mathbb E X = \\int_{-\\infty}^{\\infty} x f(dx)\n", - "$$\n", - "\n", - "In addition, let\n", - "\n", - "$$\n", - "\\bar X_n := \\frac{1}{n} \\sum_{i=1}^n X_i\n", - "$$\n", - "\n", - "TODO -- use a theorem environment (```{prf:theorem}...```)\n", - "\n", - "The law of large numbers (specifically, Kolmogorov's strong law) states that, if $\\mathbb E |X|$ is finite, then\n", - "\n", - "```{math}\n", - ":label: lln_as\n", - "\n", - "\\mathbb P \\left\\{ \\bar X_n \\to \\mu \\text{ as } n \\to \\infty \\right\\} = 1\n", - "```\n", - "\n", - "### Comments on the Theorem\n", - "\n", - "What does this last expression mean?\n", - "\n", - "Let's think about it from a simulation perspective, imagining for a moment that\n", - "our computer can generate perfect random samples (which of course [it can't](https://en.wikipedia.org/wiki/Pseudorandom_number_generator)).\n", - "\n", - "Let's also imagine that we can generate infinite sequences so that the statement $\\bar X_n \\to \\mu$ can be evaluated.\n", - "\n", - "In this setting, {eq}`lln_as` should be interpreted as meaning that the probability of the computer producing a sequence where $\\bar X_n \\to \\mu$ fails to occur\n", - "is zero." - ] - }, - { - "cell_type": "markdown", - "id": "ebc20e87", - "metadata": { - "tags": [] - }, - "source": [ - "### Illustration\n", - "\n", - "```{index} single: Law of Large Numbers; Illustration\n", - "```\n", - "\n", - "Let's now illustrate the LLN using simulation.\n", - "\n", - "When we illustrate it, we will use a key idea: the sample mean $\\bar X$ is itself a random variable.\n", - "\n", - "In a sense this is obvious but it can be easy to forget.\n", - "\n", - "The reason $\\bar X_n$ is a random variable is that it's a function of the random variables $X_1, \\ldots, X_n$.\n", - "\n", - "What we are going to do now is \n", - "\n", - "1. Pick some distribution to draw each $X_i$ from \n", - "1. Set $n$ to some large number\n", - "1. Generate the draws $X_1, \\ldots, X_n$\n", - "1. Calculate the sample mean $\\bar X_n$ and record its value in an array `sample_means`\n", - "1. Go to step 3\n", - "\n", - "We will continue the loop over steps 3-4 a total of $m$ times, where $m$ is some large integer.\n", - "\n", - "The array `sample_means` will now contain $m$ draws of the random variable $\\bar X_n$.\n", - "\n", - "If we histogram these observations of $\\bar X_n$, we should see that they are clustered around the population mean $\\mathbb E X$.\n", - "\n", - "Moreover, if we repeat the exercise with a larger value of $n$, we should see that the observations are even more tightly clustered around the population mean.\n", - "\n", - "This is, in essence, what the LLN is telling us.\n", - "\n", - "Let's run some simulations to visualize LLN" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "ced10491", - "metadata": {}, - "outputs": [], - "source": [ - "def generate_histogram(X_distribution, n, m):\n", - " fig, ax = plt.subplots(figsize=(10, 6))\n", - "\n", - " def draw_means(X_distribution, n):\n", - "\n", - " # Step 3: Generate n draws: X_1, ..., X_n\n", - " X_samples = X_distribution.rvs(size=n)\n", - "\n", - " # Step 4: Calculate the sample mean\n", - " return np.mean(X_samples)\n", - " \n", - " # Step 5: Loop m times\n", - " sample_means = [draw_means(X_distribution, n) for i in range(m)]\n", - " print(f'The mean of sample mean is {round(np.mean(sample_means),2)}')\n", - " \n", - " # Generate a histogram\n", - " ax.hist(sample_means, bins=30, alpha=0.5, density=True)\n", - " mu = X_distribution.mean()\n", - " if not np.isnan(mu):\n", - " ax.axvline(x=mu, ls=\"--\", lw=3, label=fr\"$\\mu = {mu}$\")\n", - " \n", - " ax.set_xlim(min(sample_means), max(sample_means))\n", - " ax.set_xlabel(r'$\\bar x$')\n", - " ax.set_ylabel('Density')\n", - " ax.legend()\n", - " plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "8f8b460c", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The mean of sample mean is 5.0\n" - ] - }, - { - "data": { - "image/png": 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AIEVQAgAASBGUAAAAUgQlAACAFEEJAAAgRVACAABIEZQAAABSBCUAAIAUQQkAACBFUAIAAEgpzroBAEgryuWi3wFdW9UAIF8EJQAKTllJUXx2+CFZtwFAJ2bqHQAAQIqgBAAAkGLqHdAp3Fy7MusWAIC9iBElAACAFEEJAAAgxdQ7AArO1u1N8fsXXmtR+/gRH4rSYt/vAZAfghIABWd7U1M88+qGFrURA3pFqYkQAOSJTxwAAIAUQQkAACBFUAIAAEgRlAAAAFIEJQAAgBRBCQAAIEVQAgAASBGUAAAAUgQlAACAFEEJAAAgRVACAABIEZQAAABSBCUAAICU4qwbAIC0Lrlc9NqvtFUNAPJFUAKg4JSXFMXkkYdl3QYAnZipdwAAAClGlACAnbq5dmVejnPFuMF5OQ7ArjKiBAAAkCIoAQAApAhKAAAAKe5RAqDgbGtsimVr1reoDT/swCgp8v0eAPkhKAFQcLY1NsUfV7/RojbskJ6CEgB54xMHAAAgRVACAABIEZQAAABSBCUAAIAUQQkAACBFUAIAAEgRlAAAAFIEJQAAgBRBCQAAIEVQAgAASBGUAAAAUgQlAACAFEEJAAAgpTjrBgAgLRe56FpS1KoGAPkiKAFQcLqWFsX/+cSArNsAoBMz9Q4AACBFUAIAAEgRlAAAAFIEJQAAgBRBCQAAIMWqdwAUnO2NTbHirxtb1I7t2yOKi3y/B0B+CEoAFJytjU3x8Mq/t6gNqthfUAIgbzL9xJk3b14MGzYsevToET169IhRo0bFr371q+btSZJEdXV19O3bN7p27RonnXRSrFixIsOOAQCAziDToHTIIYfETTfdFE888UQ88cQTccopp8TEiRObw9CsWbNi9uzZMXfu3Fi6dGlUVlbGuHHjYtOmTVm2DQAA7OMyDUpnnnlmnH766TF48OAYPHhw3HjjjbH//vvHkiVLIkmSmDNnTlx99dUxadKkGDJkSMyfPz82b94cd999907fs6GhITZu3NjiAQAAsDsKZrJ3Y2Nj3HvvvfH222/HqFGjYvXq1VFXVxfjx49v3qesrCzGjh0bixcv3un7zJw5M3r27Nn86N+/fz7aBwAA9iGZB6Vnn3029t9//ygrK4tLL700HnjggTjmmGOirq4uIiIqKipa7F9RUdG8bUeuuuqq2LBhQ/Nj7dq1Hdo/AACw78l81bsjjzwyli9fHm+++Wbcf//9ccEFF8SiRYuat+dyuRb7J0nSqvZeZWVlUVZW1mH9AgAA+77MR5RKS0vjiCOOiBNOOCFmzpwZxx13XNxyyy1RWVkZEdFq9Ki+vr7VKBMAAEB7yjwopSVJEg0NDVFVVRWVlZVRW1vbvG3r1q2xaNGiGD16dIYdAgAA+7pMp959/etfjwkTJkT//v1j06ZNce+998bDDz8cDz74YORyuZg6dWrU1NTEoEGDYtCgQVFTUxPdunWL8847L8u2AQCAfVymQelvf/tbTJ48OdatWxc9e/aMYcOGxYMPPhjjxo2LiIgrr7wytmzZElOmTIn169fHiBEjYuHChdG9e/cs2wYAAPZxmQalH/7wh++7PZfLRXV1dVRXV+enIQAAgCjAe5QAAACyJigBAACkCEoAAAApmf/gLACkdSstjss/OSjrNgDoxIwoAQAApAhKAAAAKYISAABAinuUAIDM3Vy7Mi/HuWLc4LwcB9j7GVECAABIMaIEQMHZ3tQUq//+dota1cH7RXEX3+8BkB+CEgAFZ+v2pvjl/1PXonbxmKooLhWUAMgPnzgAAAApghIAAECKoAQAAJDSpqC0evXq9u4DAACgYLQpKB1xxBFx8sknx1133RXvvPNOe/cEAACQqTYFpaeffjqOP/74+NrXvhaVlZVxySWXxOOPP97evQEAAGSiTUFpyJAhMXv27Hj11VfjjjvuiLq6ujjxxBPj2GOPjdmzZ8ff//739u4TAAAgb/ZoMYfi4uI4++yz47//+7/jW9/6Vrz44osxffr0OOSQQ+ILX/hCrFu3rr36BAAAyJs9CkpPPPFETJkyJfr06ROzZ8+O6dOnx4svvhi//e1v49VXX42JEye2V58AAAB5U9yWF82ePTvuuOOOeP755+P000+PBQsWxOmnnx5duvwjd1VVVcX3v//9OOqoo9q1WQAAgHxoU1CaN29efOlLX4ovfvGLUVlZucN9Dj300PjhD3+4R80BAABkoU1Bqba2Ng499NDmEaR3JUkSa9eujUMPPTRKS0vjggsuaJcmAQAA8qlN9ygNHDgwXnvttVb1N954I6qqqva4KQAAgCy1KSglSbLD+ltvvRXl5eV71BAAAEDWdmvq3bRp0yIiIpfLxTe/+c3o1q1b87bGxsb44x//GB/+8IfbtUEAOp+uJUVx8ZiqVjUAyJfdCkpPPfVURPxjROnZZ5+N0tLS5m2lpaVx3HHHxfTp09u3QwA6nVwuF91K23QbLQC0i936FPrd734XERFf/OIX45ZbbokePXp0SFMAAABZatPXdXfccUd79wEAAFAwdjkoTZo0Ke68887o0aNHTJo06X33/dnPfrbHjQEAAGRll4NSz549I5fLNf8ZAABgX7XLQem90+1MvQOgIzU2JbFuw5YWtT49u0ZRl1xGHQHQ2bTpHqUtW7ZEkiTNy4OvWbMmHnjggTjmmGNi/Pjx7dogAJ1Pw/bGuP/JV1vULh5TZSU8APKmTT84O3HixFiwYEFERLz55pvxsY99LL7zne/ExIkTY968ee3aIAAAQL61KSg9+eSTMWbMmIiIuO+++6KysjLWrFkTCxYsiO9+97vt2iAAAEC+tSkobd68Obp37x4REQsXLoxJkyZFly5dYuTIkbFmzZp2bRAAACDf2hSUjjjiiPj5z38ea9eujYceeqj5vqT6+no/QgsAAOz12hSUvvnNb8b06dPj8MMPjxEjRsSoUaMi4h+jS8cff3y7NggAAJBvbVo+6LOf/WyceOKJsW7dujjuuOOa65/85Cfj7LPPbrfmAAAAstDmdVYrKyujsrKyRe1jH/vYHjcEAACQtTYFpbfffjtuuumm+M1vfhP19fXR1NTUYvtLL73ULs0BAABkoU1B6aKLLopFixbF5MmTo0+fPpHL+aV0AABg39GmoPSrX/0q/vd//zc+/vGPt3c/AAAAmWvTqncHHnhg9OrVq717AQAAKAhtCkrXX399fPOb34zNmze3dz8AAACZa9PUu+985zvx4osvRkVFRRx++OFRUlLSYvuTTz7ZLs0BAABkoU1B6ayzzmrnNgAAAApHm4LSNddc0959AECz8uKi+L9GHNqqBgD50uYfnH3zzTfjvvvuixdffDH+9V//NXr16hVPPvlkVFRURL9+/dqzRwA6mS5dcnHQ/mVZtwFAJ9amoPTMM8/EqaeeGj179oyXX345Lr744ujVq1c88MADsWbNmliwYEF79wkAAJA3bVr1btq0aXHhhRfGqlWrory8vLk+YcKEeOSRR9qtOQAAgCy0KSgtXbo0Lrnkklb1fv36RV1d3R43BQAAkKU2BaXy8vLYuHFjq/rzzz8fBx988B43BQAAkKU2BaWJEyfGddddF9u2bYuIiFwuF6+88krMmDEjPvOZz7RrgwB0Pk1NSbz+VkOLR1NTknVbAHQibVrM4dvf/nacfvrp0bt379iyZUuMHTs26urqYtSoUXHjjTe2d48AdDLvbG+Mu/74SovaxWOqoltpmxdrBYDd0qZPnB49esRjjz0Wv/vd72LZsmXR1NQUH/nIR+LUU09t7/4AAADybreDUlNTU9x5553xs5/9LF5++eXI5XJRVVUVlZWVkSRJ5HK5jugTAAAgb3brHqUkSeKf/umf4qKLLopXX301hg4dGscee2ysWbMmLrzwwjj77LM7qk8AAIC82a0RpTvvvDMeeeSR+M1vfhMnn3xyi22//e1v46yzzooFCxbEF77whXZtEgAAIJ92a0Tpnnvuia9//eutQlJExCmnnBIzZsyIH//4x+3WHAAAQBZ2Kyg988wz8alPfWqn2ydMmBBPP/30HjcFAACQpd0KSm+88UZUVFTsdHtFRUWsX79+j5sCAADI0m4FpcbGxigu3vltTUVFRbF9+/Y9bgoAACBLu7WYQ5IkceGFF0ZZWdkOtzc0NLRLUwAAAFnaraB0wQUXfOA+VrwDAAD2drsVlO64446O6gMAAKBg7NY9SgAAAJ2BoAQAAJAiKAEAAKTs1j1KAJAPZcVF8ZmP9GtVA4B8EZQAKDhFXXJxyIHdsm4DgE7M1DsAAIAUQQkAACDF1DsgczfXrsy6BQCAFowoAQAApBhRAqDgJEkSW7Y1tqh1LSmKXC6XUUcAdDaCEgAFZ8u2xrj90dUtahePqYpupT62AMgPU+8AAABSBCUAAIAUQQkAACAl06A0c+bM+OhHPxrdu3eP3r17x1lnnRXPP/98i32SJInq6uro27dvdO3aNU466aRYsWJFRh0DAACdQaZBadGiRXHZZZfFkiVLora2NrZv3x7jx4+Pt99+u3mfWbNmxezZs2Pu3LmxdOnSqKysjHHjxsWmTZsy7BwAANiXZbp80IMPPtji+R133BG9e/eOZcuWxSc+8YlIkiTmzJkTV199dUyaNCkiIubPnx8VFRVx9913xyWXXJJF2wAAwD6uoO5R2rBhQ0RE9OrVKyIiVq9eHXV1dTF+/PjmfcrKymLs2LGxePHiHb5HQ0NDbNy4scUDAABgdxTMD1IkSRLTpk2LE088MYYMGRIREXV1dRERUVFR0WLfioqKWLNmzQ7fZ+bMmXHttdd2bLPQSdxcuzLrFgAAMlEwI0pf+cpX4plnnol77rmn1bb0L7EnSbLTX2e/6qqrYsOGDc2PtWvXdki/AADAvqsgRpT+5V/+Jf7nf/4nHnnkkTjkkEOa65WVlRHxj5GlPn36NNfr6+tbjTK9q6ysLMrKyjq2YQAAYJ+W6YhSkiTxla98JX72s5/Fb3/726iqqmqxvaqqKiorK6O2tra5tnXr1li0aFGMHj063+0CAACdRKYjSpdddlncfffd8Ytf/CK6d+/efE9Sz549o2vXrpHL5WLq1KlRU1MTgwYNikGDBkVNTU1069YtzjvvvCxbBwAA9mGZBqV58+ZFRMRJJ53Uon7HHXfEhRdeGBERV155ZWzZsiWmTJkS69evjxEjRsTChQuje/fuee4WAADoLDINSkmSfOA+uVwuqquro7q6uuMbAgAAiAJZzAEA3qu0uEucPqSyVQ0A8kVQAqDgFHfpEoMqTLEGIDu+ngMAAEgRlAAAAFIEJQAAgBRBCQAAIEVQAgAASLHqHQAFZ/PW7XH7o6tb1C4eUxXdSn1sAZAfRpQAAABSBCUAAIAUQQkAACBFUAIAAEgRlAAAAFIsHwQA0M5url3Z4ce4YtzgDj8GdGZGlAAAAFIEJQAAgBRBCQAAIEVQAgAASBGUAAAAUgQlAACAFEEJAAAgRVACAABI8YOzABSc0qIucdLgg1vVACBfBCUACk5xUZc4rv8BWbcBQCfm6zkAAIAUQQkAACBFUAIAAEgRlAAAAFIEJQAAgBSr3gFQcLZsbYz/WrKmRW3yyMOia2lRRh0B0NkISgAUnCSS2LKtsVUNAPLF1DsAAIAUQQkAACBFUAIAAEhxjxIA0GncXLsy6xaAvYQRJQAAgBRBCQAAIEVQAgAASBGUAAAAUgQlAACAFEEJAAAgRVACAABIEZQAAABSBCUAAICU4qwbAIC0kqIuMaKqV6sa8P+7uXZlXo5zxbjBeTkOFBpBCYCCU1LUJUYOOCjrNgDoxHw9BwAAkCIoAQAApAhKAAAAKe5Rgr1Qvm7gBQDorIwoAQAApBhRAqDgvLOtMX667C8tav88/JAoLynKqCMAOhtBCYCC05Qk8cbbW1vVACBfTL0DAABIMaIE7cgiCwAA+wYjSgAAACmCEgAAQIqgBAAAkCIoAQAApAhKAAAAKYISAABAiqAEAACQIigBAACkCEoAAAApghIAAECKoAQAAJBSnHUDAJBW3KVLDOvXs1UNAPJFUAKg4JQWd4mTj+qddRsAdGK+ngMAAEgRlAAAAFIEJQAAgBRBCQAAIEVQAgAASLHqHQAFp2FbY/zfz6xrUTtzWJ8oKynKqCMAOhtBCYCC05gk8eqbW1rVACBfTL0DAABIEZQAAABSBCUAAIAUQQkAACBFUAIAAEgRlAAAAFIyDUqPPPJInHnmmdG3b9/I5XLx85//vMX2JEmiuro6+vbtG127do2TTjopVqxYkU2zAABAp5FpUHr77bfjuOOOi7lz5+5w+6xZs2L27Nkxd+7cWLp0aVRWVsa4ceNi06ZNee4UAADoTDL9wdkJEybEhAkTdrgtSZKYM2dOXH311TFp0qSIiJg/f35UVFTE3XffHZdcckk+WwUAADqRgr1HafXq1VFXVxfjx49vrpWVlcXYsWNj8eLFO31dQ0NDbNy4scUDAABgd2Q6ovR+6urqIiKioqKiRb2ioiLWrFmz09fNnDkzrr322g7tjb3PzbUrs24BAIC9SMGOKL0rl8u1eJ4kSavae1111VWxYcOG5sfatWs7ukUAAGAfU7AjSpWVlRHxj5GlPn36NNfr6+tbjTK9V1lZWZSVlXV4fwAAwL6rYEeUqqqqorKyMmpra5trW7dujUWLFsXo0aMz7AyAjlbUJRdH9N6/xaOoy85nEwBAe8t0ROmtt96KF154ofn56tWrY/ny5dGrV6849NBDY+rUqVFTUxODBg2KQYMGRU1NTXTr1i3OO++8DLsGoKOVFRfFGUP7fPCOANBBMg1KTzzxRJx88snNz6dNmxYRERdccEHceeedceWVV8aWLVtiypQpsX79+hgxYkQsXLgwunfvnlXLAABAJ5BLkiTJuomOtHHjxujZs2ds2LAhevTokXU7ZMSqdwDQNleMG5x1C9BudicbFOw9SgAAAFkRlAAAAFIEJQAAgJSC/R0lADqvhu2N8evn6lvUTj26d5QVF2XUEQCdjaAEQMFpbErihfq3WtROPvLgjLoBoDMy9Q4AACBFUAIAAEgRlAAAAFIEJQAAgBRBCQAAIEVQAgAASBGUAAAAUgQlAACAFEEJAAAgRVACAABIEZQAAABSBCUAAIAUQQkAACClOOsGACCtKJeLfgd0bVUDgHwRlAAoOGUlRfHZ4Ydk3QYAnZipdwAAACmCEgAAQIqgBAAAkCIoAQAApAhKAAAAKVa9A6DgbN3eFL9/4bUWtY8f8aEoLfb9HgD5ISgBUHC2NzXFM69uaFEbMaBXlJoIAUCe+MQBAABIEZQAAABSBCUAAIAUQQkAACBFUAIAAEgRlAAAAFIEJQAAgBS/o8RO3Vy7ssOPccW4wR1+DAAA2F1GlAAAAFIEJQAAgBRBCQAAIEVQAgAASBGUAAAAUqx6B0DB6ZLLRa/9SlvVACBfBCUACk55SVFMHnlY1m0A0ImZegcAAJAiKAEAAKSYekembq5dmXULAADQihElAACAFEEJAAAgxdQ7AArOtsamWLZmfYva8MMOjJIi3+8BkB+CEgAFZ1tjU/xx9RstasMO6SkoAZA3gtJeyAIIAADQsXw1BwAAkCIoAQAApAhKAAAAKYISAABAisUcAADYqX1tEakrxg3OugX2EkaUAAAAUgQlAACAFEEJAAAgRVACAABIsZgDAACdhsUp2FVGlAAAAFIEJQAAgBRT7wAoOLnIRdeSolY1AMgXQQmAgtO1tCj+zycGZN0GAJ2YoNSO9rWbAwEAoLNyjxIAAECKoAQAAJAiKAEAAKQISgAAACkWcwCg4GxvbIoVf93YonZs3x5RXOT7PQDyo9MEpVt/+0KU77d/1m0AsAu2NjbFwyv/3qI2qGJ/QQmAvPGJAwAAkCIoAQAApAhKAAAAKYISAABASqdZzAEAAPY1N9eu7PBjXDFucIcfoxAZUQIAAEgRlAAAAFIEJQAAgBRBCQAAIMViDgAAQObysTDFO2+/tcv77hUjSt/73veiqqoqysvLY/jw4fHoo49m3RIAALAPK/ig9JOf/CSmTp0aV199dTz11FMxZsyYmDBhQrzyyitZtwYAAOyjCj4ozZ49O7785S/HRRddFEcffXTMmTMn+vfvH/Pmzcu6NQAAYB9V0Pcobd26NZYtWxYzZsxoUR8/fnwsXrx4h69paGiIhoaG5ucbNmyIiIh3Nu/6fEQAsvXOtu3R1LC5ZW3zW9FlW0F/bAHskzZu3JiX4+zO/UNtPsb/lwmSJPnAfQv6E+e1116LxsbGqKioaFGvqKiIurq6Hb5m5syZce2117aqX3f+2A7pEYD8uGFO1h0AdE5fz7qBDrBp06bo2bPn++5T0EHpXblcrsXzJEla1d511VVXxbRp05qfNzU1xRtvvBEHHXTQTl/D+9u4cWP0798/1q5dGz169Mi6HfYyrh/2hOuHPeH6YU+4fvZNSZLEpk2bom/fvh+4b0EHpQ996ENRVFTUavSovr6+1SjTu8rKyqKsrKxF7YADDuioFjuVHj16+IeCNnP9sCdcP+wJ1w97wvWz7/mgkaR3FfRiDqWlpTF8+PCora1tUa+trY3Ro0dn1BUAALCvK+gRpYiIadOmxeTJk+OEE06IUaNGxW233RavvPJKXHrppVm3BgAA7KMKPiide+658frrr8d1110X69atiyFDhsQvf/nLOOyww7JurdMoKyuLa665ptWURtgVrh/2hOuHPeH6YU+4fsglu7I2HgAAQCdS0PcoAQAAZEFQAgAASBGUAAAAUgQlAACAFEGpE5s5c2bkcrmYOnXq++536623xtFHHx1du3aNI488MhYsWNBqnzlz5sSRRx4ZXbt2jf79+8cVV1wR77zzTgd1TiFor+tn27Ztcd1118XAgQOjvLw8jjvuuHjwwQc7sHOyUl1dHblcrsWjsrLyfV+zaNGiGD58eJSXl8eAAQPiP//zP1vtc//998cxxxwTZWVlccwxx8QDDzzQUadAhjri+lmxYkV85jOficMPPzxyuVzMmTOnA8+ArHTEtXP77bfHmDFj4sADD4wDDzwwTj311Hj88cc78jTIQMEvD07HWLp0adx2220xbNiw991v3rx5cdVVV8Xtt98eH/3oR+Pxxx+Piy++OA488MA488wzIyLixz/+ccyYMSN+9KMfxejRo2PlypVx4YUXRkTEzTff3NGnQgba8/r5t3/7t7jrrrvi9ttvj6OOOioeeuihOPvss2Px4sVx/PHH5+N0yKNjjz02fv3rXzc/Lyoq2um+q1evjtNPPz0uvvjiuOuuu+L3v/99TJkyJQ4++OD4zGc+ExERf/jDH+Lcc8+N66+/Ps4+++x44IEH4pxzzonHHnssRowY0eHnQ3619/WzefPmGDBgQPzzP/9zXHHFFR3eP9lp72vn4Ycfjs9//vMxevToKC8vj1mzZsX48eNjxYoV0a9fvw4/H/IkodPZtGlTMmjQoKS2tjYZO3Zscvnll+9031GjRiXTp09vUbv88suTj3/8483PL7vssuSUU05psc+0adOSE088sV37pjC09/XTp0+fZO7cuS32mThxYnL++ee3a99k75prrkmOO+64Xd7/yiuvTI466qgWtUsuuSQZOXJk8/Nzzjkn+dSnPtVin9NOOy353Oc+t0e9Ung64vp5r8MOOyy5+eab96BDClVHXztJkiTbt29PunfvnsyfP7+tbVKATL3rhC677LI444wz4tRTT/3AfRsaGqK8vLxFrWvXrvH444/Htm3bIiLixBNPjGXLljUPOb/00kvxy1/+Ms4444z2b57Mtff1s7N9HnvssfZrmoKxatWq6Nu3b1RVVcXnPve5eOmll3a67x/+8IcYP358i9ppp50WTzzxRPP1s7N9Fi9e3P7Nk7n2vn7oPDr62tm8eXNs27YtevXq1a59ky1BqZO5995748knn4yZM2fu0v6nnXZa/OAHP4hly5ZFkiTxxBNPxI9+9KPYtm1bvPbaaxER8bnPfS6uv/76OPHEE6OkpCQGDhwYJ598csyYMaMjT4UMdMT1c9ppp8Xs2bNj1apV0dTUFLW1tfGLX/wi1q1b15GnQgZGjBgRCxYsiIceeihuv/32qKuri9GjR8frr7++w/3r6uqioqKiRa2ioiK2b9/efP3sbJ+6urqOOQky0xHXD51DPq6dGTNmRL9+/XbpS0T2Hu5R6kTWrl0bl19+eSxcuLDVN/g7841vfCPq6upi5MiRkSRJVFRUxIUXXhizZs1qnt/78MMPx4033hjf+973YsSIEfHCCy/E5ZdfHn369IlvfOMbHXlK5FFHXT+33HJLXHzxxXHUUUdFLpeLgQMHxhe/+MW44447OvJ0yMCECROa/zx06NAYNWpUDBw4MObPnx/Tpk3b4WtyuVyL50mStKrvaJ90jb1fR10/7Ps6+tqZNWtW3HPPPfHwww/v8ucjewcjSp3IsmXLor6+PoYPHx7FxcVRXFwcixYtiu9+97tRXFwcjY2NrV7TtWvX+NGPfhSbN2+Ol19+OV555ZU4/PDDo3v37vGhD30oIv7xn+HJkyfHRRddFEOHDo2zzz47ampqYubMmdHU1JTv06SDdNT1c/DBB8fPf/7zePvtt2PNmjXx5z//Ofbff/+oqqrK9ymSZ/vtt18MHTo0Vq1atcPtlZWVrUaG6uvro7i4OA466KD33Sf9bTD7nva4fuic2vPa+fa3vx01NTWxcOHCD1zgiL2PoNSJfPKTn4xnn302li9f3vw44YQT4vzzz4/ly5e/7wowJSUlccghh0RRUVHce++98elPfzq6dPnH5bN58+bmP7+rqKgokiRp/gaGvV9HXT/vKi8vj379+sX27dvj/vvvj4kTJ3b0KZGxhoaGeO6556JPnz473D5q1Kiora1tUVu4cGGccMIJUVJS8r77jB49umOapmC0x/VD59Re186///u/x/XXXx8PPvhgnHDCCR3aMxnJahUJCkN61bIZM2YkkydPbn7+/PPPJ//1X/+VrFy5MvnjH/+YnHvuuUmvXr2S1atXN+9zzTXXJN27d0/uueee5KWXXkoWLlyYDBw4MDnnnHPyeCZkoT2unyVLliT3339/8uKLLyaPPPJIcsoppyRVVVXJ+vXr83ci5MXXvva15OGHH05eeumlZMmSJcmnP/3ppHv37snLL7+cJEnr6+ell15KunXrllxxxRXJn/70p+SHP/xhUlJSktx3333N+/z+979PioqKkptuuil57rnnkptuuikpLi5OlixZkvfzo2N1xPXT0NCQPPXUU8lTTz2V9OnTJ5k+fXry1FNPJatWrcr7+dFxOuLa+da3vpWUlpYm9913X7Ju3brmx6ZNm/J+fnQcQamTS/9H94ILLkjGjh3b/PxPf/pT8uEPfzjp2rVr0qNHj2TixInJn//85xbvsW3btqS6ujoZOHBgUl5envTv3z+ZMmWK/+h2Au1x/Tz88MPJ0UcfnZSVlSUHHXRQMnny5OTVV1/N0xmQT+eee27Sp0+fpKSkJOnbt28yadKkZMWKFc3b09dPkvzj+jj++OOT0tLS5PDDD0/mzZvX6n1/+tOfJkceeWRSUlKSHHXUUcn999/f0adCBjri+lm9enUSEa0e6fdh79YR185hhx22w2vnmmuuycMZkS+5JDE3CgAA4L3cowQAAJAiKAEAAKQISgAAACmCEgAAQIqgBAAAkCIoAQAApAhKAAAAKYISAABAiqAEwD6vpqYm9t9//+ZHTU1N1i0BUOBySZIkWTcBAB3pjTfeiDfeeKP5ea9evaJXr14ZdgRAoROUAAAAUky9A2Cfdc8990R5eXm8+uqrzbWLLroohg0bFhs2bMiwMwAKnRElAPZZSZLEhz/84RgzZkzMnTs3rr322vjBD34QS5YsiX79+mXdHgAFrDjrBgCgo+Ryubjxxhvjs5/9bPTt2zduueWWePTRR4UkAD6QESUA9nkf+chHYsWKFbFw4cIYO3Zs1u0AsBdwjxIA+7SHHnoo/vznP0djY2NUVFRk3Q4AewkjSgDss5588sk46aST4tZbb4177703unXrFj/96U+zbguAvYB7lADYJ7388stxxhlnxIwZM2Ly5MlxzDHHxEc/+tFYtmxZDB8+POv2AChwRpQA2Oe88cYb8fGPfzw+8YlPxPe///3m+sSJE6OhoSEefPDBDLsDYG8gKAEAAKRYzAEAACBFUAIAAEgRlAAAAFIEJQAAgBRBCQAAIEVQAgAASBGUAAAAUgQlAACAFEEJAAAgRVACAABIEZQAAABSBCUAAICU/xex0fHoj4v//wAAAABJRU5ErkJggg==\n", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "#Step 1: Pick some distribution to draw each $X_i$ from \n", - "#Step 2: Set $n$ to some large number\n", - "generate_histogram(st.norm(loc=5, scale=2), n=50_000, m=1000)" - ] - }, - { - "cell_type": "markdown", - "id": "4e20ee45", - "metadata": {}, - "source": [ - "We can see that the distribution of $\\bar X$ is clustered around $\\mathbb E X$ as expected.\n", - "\n", - "We can vary values for `n` to see how the distribution changes" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "94b05492", - "metadata": {}, - "outputs": [], - "source": [ - "def generate_multiple_hist(X_distribution, ns, m, log_scale=False):\n", - " _, ax = plt.subplots(figsize=(10, 6))\n", - "\n", - " def draw_means(X_distribution, n):\n", - " X_samples = X_distribution.rvs(size=n)\n", - " return np.mean(X_samples)\n", - " \n", - " for n in ns:\n", - " sample_means = [draw_means(X_distribution, n) for i in range(m)]\n", - " if log_scale:\n", - " plt.xscale('symlog')\n", - " ax.hist(sample_means, bins=60, alpha=0.4, density=True, label=fr'$n = {n}$')\n", - " \n", - " mu = X_distribution.mean()\n", - " if not np.isnan(mu):\n", - " ax.axvline(x=mu, ls=\"--\", lw=3, label=fr\"$\\mu = {mu}$\")\n", - " \n", - " ax.set_xlim(min(sample_means), max(sample_means)) \n", - " ax.set_xlabel(r'$\\bar x$')\n", - " ax.set_ylabel('Density')\n", - " ax.set(title=fr'$n = {n}, m = {m}$')\n", - " ax.legend()\n", - " plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "81b7b7c0", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "generate_multiple_hist(st.norm(loc=5, scale=2), ns=[20_000, 50_000, 100_000], m=10_000)" - ] - }, - { - "cell_type": "markdown", - "id": "befa85ff", - "metadata": {}, - "source": [ - "We see that the histogram gradually converges to $\\mu$.\n", - "\n", - "You can imagine the result when extrapolating this trend for $n \\to \\infty$." - ] - }, - { - "cell_type": "markdown", - "id": "e42e4d6d", - "metadata": {}, - "source": [ - "## Breaking the LLN\n", - "\n", - "We have to pay attention to the assumptions in the statement of the LLN when we apply it.\n", - "\n", - "As indicated by {eq}`lln_as`, LLN can break when $\\mathbb E |X|$ is not finite or is not well defined.\n", - "\n", - "We can demonstrate this using a simple simulation using a [Cauchy distribution](https://en.wikipedia.org/wiki/Cauchy_distribution) for which it does not have a well-defined $\\mu$." - ] - }, - { - "cell_type": "markdown", - "id": "e44f190b", - "metadata": {}, - "source": [ - "We lost the convergence we have seen before with normal distribution" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "68405e18", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, axes = plt.subplots(1, 2, figsize=(15, 6))\n", - "\n", - "def scattered_mean(distribution, burn_in, n, jump, ax, title, color, ylog=False):\n", - " \n", - " #Set a jump to reduce simulation complexity\n", - " sample_means = [np.mean(distribution.rvs(size=i)) \n", - " for i in range(burn_in, n+1, jump)]\n", - " \n", - " ax.scatter(range(burn_in, n+1, jump), sample_means, s=10, c=color)\n", - " \n", - " #Change the y-axis to log scale if necessory\n", - " if ylog:\n", - " ax.set_yscale(\"symlog\")\n", - " ax.set_title(title, size=10)\n", - " ax.set_xlabel(r\"$n$\", size=12)\n", - " ax.set_ylabel(r\"$\\bar x$\", size=12)\n", - " yabs_max = max(ax.get_ylim(), key=abs)\n", - " ax.set_ylim(ymin=-yabs_max, ymax=yabs_max)\n", - " return ax\n", - "\n", - "scattered_mean(distribution=st.cauchy(), \n", - " burn_in=1000, \n", - " n=1_000_000, \n", - " ax=axes[0],\n", - " jump=2000,\n", - " title=\"Cauchy Distribution\",\n", - " color='#1f77b4',\n", - " ylog=True)\n", - "\n", - "scattered_mean(distribution=st.norm(), \n", - " burn_in=1000, \n", - " n=1_000_000,\n", - " ax=axes[1],\n", - " jump=2000,\n", - " title=\"Normal Distribution\",\n", - " color='#ff7f0e')\n", - "\n", - "fig.suptitle('Sample Mean with Different Sample Size')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "8b791a86", - "metadata": {}, - "source": [ - "We can see that unlike normal distribution, Cauchy distribution does not have the convergence that LLN implies.\n", - "\n", - "It is also not hard to conjecture that LLN can be broken when the IID assumption is violated." - ] - }, - { - "cell_type": "markdown", - "id": "8a9f6739", - "metadata": {}, - "source": [ - "Let's go through a very simple example where LLN fails with IID violated:\n", - "\n", - "Assume\n", - "\n", - "$$\n", - "X_1 \\sim \\mathcal{N}(0,1)\n", - "$$\n", - "\n", - "In addition, assume\n", - "\n", - "$$\n", - "X_t = X_{t-1} \\quad \\text{for} \\quad t = 2, ..., n\n", - "$$\n", - "\n", - "We can then see that \n", - "\n", - "$$\n", - "\\bar X_n := \\frac{1}{n} \\sum_{t=1}^n X_i = X_1 \\sim \\mathcal{N}(0,1)\n", - "$$\n", - "\n", - "Therefore, the distribution of the mean of X follows $\\mathcal{N}(0,1)$.\n", - "\n", - "However,\n", - "\n", - "$$\n", - "\\mathbb E X_t = \\mathbb E X_1 = 0\n", - "$$\n", - "\n", - "which violates {eq}`exp`, and thus breaks LLN.\n", - "\n", - "```{note}\n", - "Although in this case, the violation of IID breaks LLN, it is not always the case for correlated data (TODO: Link to Exercise)\n", - "```" - ] - }, - { - "cell_type": "markdown", - "id": "73902f5a", - "metadata": {}, - "source": [ - "## CLT\n", - "\n", - "```{index} single: Central Limit Theorem\n", - "```\n", - "\n", - "Next, we turn to the central limit theorem, which tells us about the distribution of the deviation between sample averages and population means.\n", - "\n", - "### Statement of the Theorem\n", - "\n", - "The central limit theorem is one of the most remarkable results in all of mathematics.\n", - "\n", - "In the IID setting, it tells us the following:\n", - "\n", - "TODO use a theorem environment (```{prf:theorem...```)\n", - "\n", - "(statement_clt)=\n", - "If the sequence $X_1, \\ldots, X_n$ is IID, with common mean\n", - "$\\mu$ and common variance $\\sigma^2 \\in (0, \\infty)$, then\n", - "\n", - "```{math}\n", - ":label: lln_clt\n", - "\n", - "\\sqrt{n} ( \\bar X_n - \\mu ) \\stackrel { d } {\\to} N(0, \\sigma^2)\n", - "\\quad \\text{as} \\quad\n", - "n \\to \\infty\n", - "```\n", - "\n", - "Here $\\stackrel { d } {\\to} N(0, \\sigma^2)$ indicates [convergence in distribution](https://en.wikipedia.org/wiki/Convergence_of_random_variables#Convergence_in_distribution) to a centered (i.e, zero mean) normal with standard deviation $\\sigma$.\n", - "\n", - "### Intuition\n", - "\n", - "```{index} single: Central Limit Theorem; Intuition\n", - "```\n", - "\n", - "The striking implication of the CLT is that for **any** distribution with\n", - "finite second moment, the simple operation of adding independent\n", - "copies **always** leads to a Gaussian curve." - ] - }, - { - "cell_type": "markdown", - "id": "5b7ca292", - "metadata": { - "tags": [] - }, - "source": [ - "### Simulation 1\n", - "\n", - "Since the CLT seems almost magical, running simulations that verify its implications is one good way to build intuition.\n", - "\n", - "To this end, we now perform the following simulation\n", - "\n", - "1. Choose an arbitrary distribution $F$ for the underlying observations $X_i$.\n", - "1. Generate independent draws of $Y_n := \\sqrt{n} ( \\bar X_n - \\mu )$.\n", - "1. Use these draws to compute some measure of their distribution --- such as a histogram.\n", - "1. Compare the latter to $N(0, \\sigma^2)$.\n", - "\n", - "Here's some code that does exactly this for the exponential distribution\n", - "$F(x) = 1 - e^{- \\lambda x}$.\n", - "\n", - "(Please experiment with other choices of $F$, but remember that, to conform with the conditions of the CLT, the distribution must have a finite second moment.)\n", - "\n", - "(sim_one)=" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "dc6bf8f3", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Set parameters\n", - "n = 250 # Choice of n\n", - "k = 1_000_000 # Number of draws of Y_n\n", - "distribution = st.expon(2) # Exponential distribution, λ = 1/2\n", - "μ, σ = distribution.mean(), distribution.std()\n", - "\n", - "# Draw underlying RVs. Each row contains a draw of X_1,..,X_n\n", - "data = distribution.rvs((k, n))\n", - "# Compute mean of each row, producing k draws of \\bar X_n\n", - "sample_means = data.mean(axis=1)\n", - "# Generate observations of Y_n\n", - "Y = np.sqrt(n) * (sample_means - μ)\n", - "\n", - "# Plot\n", - "fig, ax = plt.subplots(figsize=(10, 6))\n", - "xmin, xmax = -3 * σ, 3 * σ\n", - "ax.set_xlim(xmin, xmax)\n", - "ax.hist(Y, bins=60, alpha=0.4, density=True)\n", - "xgrid = np.linspace(xmin, xmax, 200)\n", - "ax.plot(xgrid, st.norm.pdf(xgrid, scale=σ), 'k-', lw=2, label='$N(0, \\sigma^2)$')\n", - "ax.legend()\n", - "\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "0e81bddf", - "metadata": {}, - "source": [ - "(Notice the absence of for loops --- every operation is vectorized, meaning that the major calculations are all shifted to optimized C code.)\n", - "\n", - "The fit to the normal density is already tight and can be further improved by increasing `n`." - ] - }, - { - "cell_type": "markdown", - "id": "34a77889", - "metadata": {}, - "source": [ - "## Exercises" - ] - }, - { - "cell_type": "markdown", - "id": "f80f94a3", - "metadata": {}, - "source": [ - "## Ex 1" - ] - }, - { - "cell_type": "markdown", - "id": "b9537695", - "metadata": {}, - "source": [ - "Repeat the simulation in (TODO: Add a reference to simulation one) with [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution)." - ] - }, - { - "cell_type": "markdown", - "id": "2db66fc9", - "metadata": {}, - "source": [ - "Solution:" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "8c3c06ab", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Set parameters\n", - "n = 250 # Choice of n\n", - "k = 1_000_000 # Number of draws of Y_n\n", - "distribution = st.beta(2,2) # Exponential distribution, λ = 1/2\n", - "μ, σ = distribution.mean(), distribution.std()\n", - "\n", - "# Draw underlying RVs. Each row contains a draw of X_1,..,X_n\n", - "data = distribution.rvs((k, n))\n", - "# Compute mean of each row, producing k draws of \\bar X_n\n", - "sample_means = data.mean(axis=1)\n", - "# Generate observations of Y_n\n", - "Y = np.sqrt(n) * (sample_means - μ)\n", - "\n", - "# Plot\n", - "fig, ax = plt.subplots(figsize=(10, 6))\n", - "xmin, xmax = -3 * σ, 3 * σ\n", - "ax.set_xlim(xmin, xmax)\n", - "ax.hist(Y, bins=60, alpha=0.4, density=True)\n", - "xgrid = np.linspace(xmin, xmax, 200)\n", - "ax.plot(xgrid, st.norm.pdf(xgrid, scale=σ), 'k-', lw=2, label='$N(0, \\sigma^2)$')\n", - "ax.legend()\n", - "\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "dc5410ce", - "metadata": {}, - "source": [ - "## Ex 2" - ] - }, - { - "cell_type": "markdown", - "id": "ba22dc50", - "metadata": {}, - "source": [ - "Although NumPy doesn't give us a `bernoulli` function, we can generate a draw of $X$ using NumPy via" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "904b490a", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0\n" - ] - } - ], - "source": [ - "U = np.random.rand()\n", - "X = 1 if U < p else 0\n", - "print(X)" - ] - }, - { - "cell_type": "markdown", - "id": "d10e3d75", - "metadata": {}, - "source": [ - "Explain why this provides a random variable $X$ with the right distribution." - ] - }, - { - "cell_type": "markdown", - "id": "fd00362c", - "metadata": {}, - "source": [ - "Solution:" - ] - }, - { - "cell_type": "markdown", - "id": "c9dc395c", - "metadata": {}, - "source": [ - "We can write $X$ as $X = \\mathbf 1\\{U < p\\}$ where $\\mathbf 1$ is the [indicator function](https://en.wikipedia.org/wiki/Indicator_function) (i.e., 1 if the statement is true and zero otherwise).\n", - "\n", - "Here we generated a uniform draw $U$ on $[0,1]$ and then used the fact that\n", - "\n", - "$$\n", - "\\mathbb P\\{0 \\leq U < p\\} = p - 0 = p\n", - "$$\n", - "\n", - "This means that $X = \\mathbf 1\\{U < p\\}$ has the right distribution." - ] - }, - { - "cell_type": "markdown", - "id": "53659cd9", - "metadata": {}, - "source": [ - "## Ex 3" - ] - }, - { - "cell_type": "markdown", - "id": "fe57b8aa", - "metadata": {}, - "source": [ - "We mentioned above that it is possible for LLN to hold when IID is violated.\n", - "\n", - "Let's investigate this claim further.\n", - "\n", - "Assume we have a AR(1) process as below:\n", - "$$\n", - "X_{t+1} = \\alpha + \\beta X_t + \\sigma \\epsilon _{t+1}\n", - "$$\n", - "\n", - "$$\n", - "X_0 \\sim \\mathcal{N} \\left(\\frac{\\alpha}{1-\\beta}, \\frac{\\sigma^2}{1-\\beta^2}\\right)\n", - "$$\n", - "\n", - "where $\\epsilon_t \\sim \\mathcal{N}(0,1)$\n", - "\n", - "1. Prove this process violated the independence assumption but not the identically distributed assumption;\n", - "2. Show LLN holds using simulations with $\\alpha = 0.8$, $\\beta = 0.2$." - ] - }, - { - "cell_type": "markdown", - "id": "fb921dc0", - "metadata": {}, - "source": [ - "Solution:\n", - "\n", - "1. \n", - "\n", - "Given X_{t+1} is dependent on X_t, this process is not independent.\n", - "\n", - "To check whether it is identically distributed, we need to check whether the distribution in $T={0...n}$\n", - "\n", - "Let's verify the expectation and variance of this AR(1) process using pen and paper first.\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "\\mathbb E X_{t+1} &= \\alpha + \\beta \\mathbb E X_t \\\\\n", - "&= \\alpha + \\beta \\frac{\\alpha}{1-\\beta} \\\\\n", - "&= \\frac{\\alpha}{1-\\beta}\n", - "\\end{aligned}\n", - "$$ \n", - "\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "Var(X_t+1) &= \\beta^2 Var(X_{t}) + \\sigma^2\\\\\n", - "&= \\frac{\\beta^2\\sigma^2}{1-\\beta^2} + \\sigma^2 \\\\\n", - "&= \\frac{\\sigma^2}{1-\\beta^2}\n", - "\\end{aligned}\n", - "$$ \n", - "\n", - "We find that expectation and variance are the same $t = 0, ..., n$.\n", - "\n", - "Given both $X_0$ and $\\epsilon _{0}$ are normally distributed and independent from each other, the weighted sum of the two normally distributed random variables is also normally distributed.\n", - "\n", - "This holds true for all $X_t$ and $\\epsilon _{t}$ where $t = 0, ..., n$\n", - "\n", - "Therefore, \n", - "\n", - "$$\n", - "X_t \\sim \\mathcal{N} \\left(\\frac{\\alpha}{1-\\beta}, \\frac{\\sigma^2}{1-\\beta^2}\\right) \\quad t = 0, ..., n\n", - "$$ \n", - "\n", - "\n", - "We can conclude this AR(1) process violates the independence assumption but is identically distributed.\n", - "\n", - "2." - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "4bcd7f2d", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "σ = 10\n", - "α = 0.8\n", - "β = 0.2\n", - "n = 100_000\n", - "\n", - "fig, ax = plt.subplots(figsize=(10, 6))\n", - "x = np.ones(n)\n", - "x[0] = st.norm.rvs(α/(1-β), α**2/(1-β**2))\n", - "ϵ = st.norm.rvs(size=n+1)\n", - "means = np.ones(n)\n", - "for t in range(n-1):\n", - " x[t+1] = α + β * x[t] + σ * ϵ[t+1]\n", - " means[t+1] = np.mean(x[:t+1])\n", - "\n", - "\n", - "ax.scatter(range(100, n), means[100:n], s=10, alpha=0.5)\n", - "\n", - "ax.set_xlabel(r\"$n$\", size=12)\n", - "ax.set_ylabel(r\"$\\bar x$\", size=12)\n", - "yabs_max = max(ax.get_ylim(), key=abs)\n", - "ax.axhline(y=α/(1-β), ls=\"--\", lw=3, label=r\"$\\mu = \\frac{\\alpha}{1-\\beta}$\",color = 'black')\n", - "\n", - "plt.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "a3111332", - "metadata": {}, - "source": [ - "```{solution-end}\n", - "```" - ] - }, - { - "cell_type": "markdown", - "id": "96f9e087", - "metadata": {}, - "source": [ - "We see the convergence of $\\bar x$ around $\\mu$ even when the independence assumption is violated." - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/in-work/lln_clt.md b/in-work/lln_clt.md index 88cf01eab..2a42014bc 100644 --- a/in-work/lln_clt.md +++ b/in-work/lln_clt.md @@ -256,28 +256,27 @@ We can vary values for `n` to see how the distribution changes ```{code-cell} ipython3 def generate_multiple_hist(X_distribution, ns, m, log_scale=False): - _, ax = plt.subplots(figsize=(10, 6)) + _, ax = plt.subplots(figsize=(10, 6)) - def draw_means(X_distribution, n): - X_samples = X_distribution.rvs(size=n) - return np.mean(X_samples) - - for n in ns: - sample_means = [draw_means(X_distribution, n) for i in range(m)] - if log_scale: - plt.xscale('symlog') - ax.hist(sample_means, bins=60, alpha=0.4, density=True, label=fr'$n = {n}$') - - mu = X_distribution.mean() - if not np.isnan(mu): - ax.axvline(x=mu, ls="--", lw=3, label=fr"$\mu = {mu}$") + def draw_means(X_distribution, n): + X_samples = X_distribution.rvs(size=n) + return np.mean(X_samples) - ax.set_xlim(min(sample_means), max(sample_means)) - ax.set_xlabel(r'$\bar x$') - ax.set_ylabel('Density') - ax.set(title=fr'$n = {n}, m = {m}$') - ax.legend() - plt.show() + for n in ns: + sample_means = [draw_means(X_distribution, n) for i in range(m)] + if log_scale: + plt.xscale('symlog') + ax.hist(sample_means, bins=40, alpha=0.4, density=True, label=fr'$n = {n}$') + + mu = X_distribution.mean() + if not np.isnan(mu): + ax.axvline(x=mu, ls="--", lw=3, label=fr"$\mu = {mu}$") + + ax.set_xlim(min(sample_means), max(sample_means)) + ax.set_xlabel(r'$\bar x$') + ax.set_ylabel('Density') + ax.legend() + plt.show() ``` ```{code-cell} ipython3 @@ -308,20 +307,20 @@ fig, axes = plt.subplots(1, 2, figsize=(15, 6)) def scattered_mean(distribution, burn_in, n, jump, ax, title, color, ylog=False): #Set a jump to reduce simulation complexity - sample_means = [np.mean(distribution.rvs(size=i)) + sample_means = [np.mean(distribution.rvs(size=i)) for i in range(burn_in, n+1, jump)] - ax.scatter(range(burn_in, n+1, jump), sample_means, s=10, c=color) + ax.scatter(range(burn_in, n+1, jump), sample_means, s=10, c=color) - #Change the y-axis to log scale if necessory - if ylog: - ax.set_yscale("symlog") - ax.set_title(title, size=10) - ax.set_xlabel(r"$n$", size=12) - ax.set_ylabel(r"$\bar x$", size=12) - yabs_max = max(ax.get_ylim(), key=abs) - ax.set_ylim(ymin=-yabs_max, ymax=yabs_max) - return ax + #Change the y-axis to log scale if necessory + if ylog: + ax.set_yscale("symlog") + ax.set_title(title, size=10) + ax.set_xlabel(r"$n$", size=12) + ax.set_ylabel(r"$\bar x$", size=12) + yabs_max = max(ax.get_ylim(), key=abs) + ax.set_ylim(ymin=-yabs_max, ymax=yabs_max) + return ax scattered_mean(distribution=st.cauchy(), burn_in=1000, @@ -340,7 +339,7 @@ scattered_mean(distribution=st.norm(), title="Normal Distribution", color='#ff7f0e') -fig.suptitle('Sample Mean with Different Sample Size') +fig.suptitle('Sample Mean with Different Sample Sizes') plt.show() ``` @@ -601,7 +600,7 @@ $$ We find that expectation and variance are the same $t = 0, ..., n$. -Given both $X_0$ and $\epsilon _{0}$ are normally distributed and independent from each other, the weighted sum of the two normally distributed random variables is also normally distributed. +Given both $X_0$ and $\epsilon _{0}$ are normally distributed and independent from each other, the weighted sum is also normally distributed. This holds true for all $X_t$ and $\epsilon _{t}$ where $t = 0, ..., n$ @@ -627,9 +626,10 @@ x = np.ones(n) x[0] = st.norm.rvs(α/(1-β), α**2/(1-β**2)) ϵ = st.norm.rvs(size=n+1) means = np.ones(n) +means[0] = x[0] for t in range(n-1): - x[t+1] = α + β * x[t] + σ * ϵ[t+1] - means[t+1] = np.mean(x[:t+1]) + x[t+1] = α + β * x[t] + σ * ϵ[t+1] + means[t+1] = np.mean(x[:t+1]) ax.scatter(range(100, n), means[100:n], s=10, alpha=0.5) From 9449b38d04bbfcfcc9d0771d6ea0db6d38a90825 Mon Sep 17 00:00:00 2001 From: Humphrey Yang Date: Fri, 3 Feb 2023 18:49:46 +1100 Subject: [PATCH 10/12] update theorem env --- in-work/lln_clt.md | 64 ++++++++++++++++++++++++---------------------- 1 file changed, 34 insertions(+), 30 deletions(-) diff --git a/in-work/lln_clt.md b/in-work/lln_clt.md index 2a42014bc..037db8945 100644 --- a/in-work/lln_clt.md +++ b/in-work/lln_clt.md @@ -158,8 +158,8 @@ $$ \bar X_n := \frac{1}{n} \sum_{i=1}^n X_i $$ -TODO -- use a theorem environment (```{prf:theorem}...```) +````{prf:theorem} The law of large numbers (specifically, Kolmogorov's strong law) states that, if $\mathbb E |X|$ is finite, then ```{math} @@ -167,6 +167,7 @@ The law of large numbers (specifically, Kolmogorov's strong law) states that, if \mathbb P \left\{ \bar X_n \to \mu \text{ as } n \to \infty \right\} = 1 ``` +```` ### Comments on the Theorem @@ -287,7 +288,6 @@ We see that the histogram gradually converges to $\mu$. You can imagine the result when extrapolating this trend for $n \to \infty$. -+++ ## Breaking the LLN @@ -297,7 +297,6 @@ As indicated by {eq}`lln_as`, LLN can break when $\mathbb E |X|$ is not finite o We can demonstrate this using a simple simulation using a [Cauchy distribution](https://en.wikipedia.org/wiki/Cauchy_distribution) for which it does not have a well-defined $\mu$. -+++ We lost the convergence we have seen before with normal distribution @@ -347,7 +346,7 @@ We can see that unlike normal distribution, Cauchy distribution does not have th It is also not hard to conjecture that LLN can be broken when the IID assumption is violated. -+++ + Let's go through a very simple example where LLN fails with IID violated: @@ -383,7 +382,7 @@ which violates {eq}`exp`, and thus breaks LLN. Although in this case, the violation of IID breaks LLN, it is not always the case for correlated data (TODO: Link to Exercise) ``` -+++ + ## CLT @@ -398,9 +397,10 @@ The central limit theorem is one of the most remarkable results in all of mathem In the IID setting, it tells us the following: -TODO use a theorem environment (```{prf:theorem...```) -(statement_clt)= +````{prf:theorem} +:label: statement_clt + If the sequence $X_1, \ldots, X_n$ is IID, with common mean $\mu$ and common variance $\sigma^2 \in (0, \infty)$, then @@ -411,6 +411,7 @@ $\mu$ and common variance $\sigma^2 \in (0, \infty)$, then \quad \text{as} \quad n \to \infty ``` +```` Here $\stackrel { d } {\to} N(0, \sigma^2)$ indicates [convergence in distribution](https://en.wikipedia.org/wiki/Convergence_of_random_variables#Convergence_in_distribution) to a centered (i.e, zero mean) normal with standard deviation $\sigma$. @@ -423,8 +424,6 @@ The striking implication of the CLT is that for **any** distribution with finite second moment, the simple operation of adding independent copies **always** leads to a Gaussian curve. -+++ {"tags": []} - ### Simulation 1 Since the CLT seems almost magical, running simulations that verify its implications is one good way to build intuition. @@ -473,21 +472,21 @@ plt.show() The fit to the normal density is already tight and can be further improved by increasing `n`. -+++ ## Exercises -+++ -## Ex 1 -+++ +```{exercise} +:label: lln_ex1 Repeat the simulation in (TODO: Add a reference to simulation one) with [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution). -+++ +``` -Solution: +```{solution-start} +:class: dropdown +``` ```{code-cell} ipython3 # Set parameters @@ -515,9 +514,11 @@ ax.legend() plt.show() ``` -## Ex 2 +```{solution-end} +``` -+++ +```{exercise} +:label: lln_ex2 Although NumPy doesn't give us a `bernoulli` function, we can generate a draw of $X$ using NumPy via @@ -529,11 +530,11 @@ print(X) Explain why this provides a random variable $X$ with the right distribution. -+++ - -Solution: +``` -+++ +```{solution-start} lln_ex2 +:class: dropdown +``` We can write $X$ as $X = \mathbf 1\{U < p\}$ where $\mathbf 1$ is the [indicator function](https://en.wikipedia.org/wiki/Indicator_function) (i.e., 1 if the statement is true and zero otherwise). @@ -545,11 +546,13 @@ $$ This means that $X = \mathbf 1\{U < p\}$ has the right distribution. -+++ +```{solution-end} +``` + -## Ex 3 -+++ +```{exercise} +:label: lln_ex3 We mentioned above that it is possible for LLN to hold when IID is violated. @@ -569,9 +572,11 @@ where $\epsilon_t \sim \mathcal{N}(0,1)$ 1. Prove this process violated the independence assumption but not the identically distributed assumption; 2. Show LLN holds using simulations with $\alpha = 0.8$, $\beta = 0.2$. -+++ +``` -Solution: +```{solution-start} lln_ex3 +:class: dropdown +``` 1. @@ -643,9 +648,8 @@ plt.legend() plt.show() ``` -```{solution-end} -``` +We see the convergence of $\bar x$ around $\mu$ even when the independence assumption is violated. -+++ -We see the convergence of $\bar x$ around $\mu$ even when the independence assumption is violated. +```{solution-end} +``` From a86b5ac030dc9fdb841e877eb9462e0bb0751ef9 Mon Sep 17 00:00:00 2001 From: Humphrey Yang Date: Sat, 4 Feb 2023 23:08:38 +1100 Subject: [PATCH 11/12] add labels --- in-work/lln_clt.md | 13 +++++++++---- 1 file changed, 9 insertions(+), 4 deletions(-) diff --git a/in-work/lln_clt.md b/in-work/lln_clt.md index 037db8945..652f84834 100644 --- a/in-work/lln_clt.md +++ b/in-work/lln_clt.md @@ -239,8 +239,8 @@ def generate_histogram(X_distribution, n, m): ax.axvline(x=mu, ls="--", lw=3, label=fr"$\mu = {mu}$") ax.set_xlim(min(sample_means), max(sample_means)) - ax.set_xlabel(r'$\bar x$') - ax.set_ylabel('Density') + ax.set_xlabel(r'$\bar x$', size=12) + ax.set_ylabel('density', size=12) ax.legend() plt.show() ``` @@ -274,8 +274,8 @@ def generate_multiple_hist(X_distribution, ns, m, log_scale=False): ax.axvline(x=mu, ls="--", lw=3, label=fr"$\mu = {mu}$") ax.set_xlim(min(sample_means), max(sample_means)) - ax.set_xlabel(r'$\bar x$') - ax.set_ylabel('Density') + ax.set_xlabel(r'$\bar x$', size=12) + ax.set_ylabel('density', size=12) ax.legend() plt.show() ``` @@ -463,6 +463,9 @@ ax.set_xlim(xmin, xmax) ax.hist(Y, bins=60, alpha=0.4, density=True) xgrid = np.linspace(xmin, xmax, 200) ax.plot(xgrid, st.norm.pdf(xgrid, scale=σ), 'k-', lw=2, label='$N(0, \sigma^2)$') +ax.set_xlabel(r"$Y$", size=12) +ax.set_ylabel(r"$density$", size=12) + ax.legend() plt.show() @@ -507,6 +510,8 @@ fig, ax = plt.subplots(figsize=(10, 6)) xmin, xmax = -3 * σ, 3 * σ ax.set_xlim(xmin, xmax) ax.hist(Y, bins=60, alpha=0.4, density=True) +ax.set_xlabel(r"$Y$", size=12) +ax.set_ylabel(r"$density$", size=12) xgrid = np.linspace(xmin, xmax, 200) ax.plot(xgrid, st.norm.pdf(xgrid, scale=σ), 'k-', lw=2, label='$N(0, \sigma^2)$') ax.legend() From 9c05f414a1675751e571fd41b9db62740f81d34b Mon Sep 17 00:00:00 2001 From: Humphrey Yang Date: Sun, 5 Feb 2023 23:39:07 +1100 Subject: [PATCH 12/12] integrate comments --- in-work/lln_clt.md | 64 ++++++++++++++++++++-------------------------- 1 file changed, 28 insertions(+), 36 deletions(-) diff --git a/in-work/lln_clt.md b/in-work/lln_clt.md index 652f84834..9aecbe756 100644 --- a/in-work/lln_clt.md +++ b/in-work/lln_clt.md @@ -24,12 +24,7 @@ The lecture is based around simulations that show the LLN and CLT in action. We also demonstrate how the LLN and CLT break down when the assumptions they are based on do not hold. -In addition, we examine several useful extensions of the classical theorems, such as - -* The delta method, for smooth functions of random variables, and -* the multivariate case. - -Some of these extensions are presented as exercises. +This lecture will focus on the univariable case to provide the intuitions for proofs and the generalization to multivariate case [later](https://python.quantecon.org/lln_clt.html#the-multivariate-case). We'll need the following imports: @@ -42,7 +37,6 @@ import scipy.stats as st ## Relationships - The LLN gives conditions under which sample moments converge to population moments as sample size increases. The CLT provides information about the rate at which sample moments converge to population moments as sample size increases. @@ -113,7 +107,7 @@ $$ which, in this case, is the fraction of draws that equal one (the number of heads divided by $n$). -Thus, the LLN tells us that +Thus, the LLN tells us that for the Bernoulli trials above ```{math} :label: exp @@ -122,9 +116,7 @@ Thus, the LLN tells us that \qquad (n \to \infty) ``` -This is exactly what we illustrated in the code above. - -+++ {"jp-MarkdownHeadingCollapsed": true, "tags": []} +This is exactly what we illustrated in the code. (lln_ksl)= ### Statement of the LLN @@ -284,7 +276,7 @@ def generate_multiple_hist(X_distribution, ns, m, log_scale=False): generate_multiple_hist(st.norm(loc=5, scale=2), ns=[20_000, 50_000, 100_000], m=10_000) ``` -We see that the histogram gradually converges to $\mu$. +The histogram gradually converges to $\mu$ as the sample size n increases. You can imagine the result when extrapolating this trend for $n \to \infty$. @@ -311,13 +303,13 @@ def scattered_mean(distribution, burn_in, n, jump, ax, title, color, ylog=False) ax.scatter(range(burn_in, n+1, jump), sample_means, s=10, c=color) - #Change the y-axis to log scale if necessory + #Change the y-axis to log scale if necessary if ylog: ax.set_yscale("symlog") ax.set_title(title, size=10) ax.set_xlabel(r"$n$", size=12) ax.set_ylabel(r"$\bar x$", size=12) - yabs_max = max(ax.get_ylim(), key=abs) + yabs_max = max(ax.get_ylim()) ax.set_ylim(ymin=-yabs_max, ymax=yabs_max) return ax @@ -342,47 +334,47 @@ fig.suptitle('Sample Mean with Different Sample Sizes') plt.show() ``` -We can see that unlike normal distribution, Cauchy distribution does not have the convergence that LLN implies. - -It is also not hard to conjecture that LLN can be broken when the IID assumption is violated. - +We find that unlike normal distribution, Cauchy distribution does not have the convergence that LLN implies. +It is also not hard to conjecture that LLN can be broken when the independence assumption is violated. Let's go through a very simple example where LLN fails with IID violated: Assume $$ -X_1 \sim \mathcal{N}(0,1) +X_0 \sim \mathcal{N}(0,1) $$ In addition, assume $$ -X_t = X_{t-1} \quad \text{for} \quad t = 2, ..., n +X_t = X_{t-1} \quad \text{for} \quad t = 1, ..., n $$ We can then see that $$ -\bar X_n := \frac{1}{n} \sum_{t=1}^n X_i = X_1 \sim \mathcal{N}(0,1) +\bar X_n := \frac{1}{n} \sum_{t=1}^n X_i = X_0 \sim \mathcal{N}(0,1) $$ -Therefore, the distribution of the mean of X follows $\mathcal{N}(0,1)$. +Therefore, the distribution of the mean of $X$ follows $\mathcal{N}(0,1)$. However, $$ -\mathbb E X_t = \mathbb E X_1 = 0 +\mathbb E X_t = \mathbb E X_0 = 0 $$ -which violates {eq}`exp`, and thus breaks LLN. +Since the distribution of $\bar X$ follows a standard normal distribution, but the expectation $\mathbb E X_t$ is a single number. -```{note} -Although in this case, the violation of IID breaks LLN, it is not always the case for correlated data (TODO: Link to Exercise) -``` +This violates {eq}`exp`, and thus breaks LLN. +```{note} +Although in this case, the violation of IID breaks LLN, it is not always the case for correlated data. +We will show an example in the [exercise](lln_ex3). +``` ## CLT @@ -413,7 +405,7 @@ n \to \infty ``` ```` -Here $\stackrel { d } {\to} N(0, \sigma^2)$ indicates [convergence in distribution](https://en.wikipedia.org/wiki/Convergence_of_random_variables#Convergence_in_distribution) to a centered (i.e, zero mean) normal with standard deviation $\sigma$. +Here $\stackrel { d } {\to} N(0, \sigma^2)$ indicates [convergence in distribution](https://en.wikipedia.org/wiki/Convergence_of_random_variables#Convergence_in_distribution) to a centered (i.e., zero mean) normal with standard deviation $\sigma$. ### Intuition @@ -421,7 +413,7 @@ Here $\stackrel { d } {\to} N(0, \sigma^2)$ indicates [convergence in distributi ``` The striking implication of the CLT is that for **any** distribution with -finite second moment, the simple operation of adding independent +finite [second moment](https://en.wikipedia.org/wiki/Moment_(mathematics)), the simple operation of adding independent copies **always** leads to a Gaussian curve. ### Simulation 1 @@ -441,7 +433,6 @@ $F(x) = 1 - e^{- \lambda x}$. (Please experiment with other choices of $F$, but remember that, to conform with the conditions of the CLT, the distribution must have a finite second moment.) (sim_one)= - ```{code-cell} ipython3 # Set parameters n = 250 # Choice of n @@ -483,8 +474,9 @@ The fit to the normal density is already tight and can be further improved by in ```{exercise} :label: lln_ex1 -Repeat the simulation in (TODO: Add a reference to simulation one) with [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution). +Repeat the simulation in [simulation 1](sim_one) with [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution). +You can choose any $\alpha > 0$ and $\beta > 0$. ``` ```{solution-start} @@ -495,7 +487,7 @@ Repeat the simulation in (TODO: Add a reference to simulation one) with [beta di # Set parameters n = 250 # Choice of n k = 1_000_000 # Number of draws of Y_n -distribution = st.beta(2,2) # Exponential distribution, λ = 1/2 +distribution = st.beta(2,2) # We chose Beta(2, 2) as an example μ, σ = distribution.mean(), distribution.std() # Draw underlying RVs. Each row contains a draw of X_1,..,X_n @@ -559,7 +551,7 @@ This means that $X = \mathbf 1\{U < p\}$ has the right distribution. ```{exercise} :label: lln_ex3 -We mentioned above that it is possible for LLN to hold when IID is violated. +We mentioned above that LLN can still hold sometimes when IID is violated. Let's investigate this claim further. @@ -583,9 +575,9 @@ where $\epsilon_t \sim \mathcal{N}(0,1)$ :class: dropdown ``` -1. +**Q1 Solution** -Given X_{t+1} is dependent on X_t, this process is not independent. +Given $X_{t+1}$ is dependent on the value of $X_t$, this process is not independent. To check whether it is identically distributed, we need to check whether the distribution in $T={0...n}$ @@ -623,7 +615,7 @@ $$ We can conclude this AR(1) process violates the independence assumption but is identically distributed. -2. +**Q2 Solution** ```{code-cell} ipython3 σ = 10