Point Process

A modern C++ implementation of point process models for heart rate variability (HRV) analysis. Based on the MATLAB software by Riccardo Barbieri and Luca Citi (http://users.neurostat.mit.edu/barbieri/pphrv).

Key Features:

• Fast C++ implementation with Python bindings
• Multiple distribution models (Inverse Gaussian, Gaussian, LogNormal)
• State-space regression and spectral analysis
• Easy-to-use Python API with NumPy/SciPy integration
• Cross-platform support (Linux, Windows, macOS)
• Distributed as pre-built wheels via PyPI

Reference Papers:

• A point-process model of human heartbeat intervals: new definitions of heart rate and heart rate variability
• The time-rescaling theorem and its application to neural spike train data analysis

Installation

From PyPI (Recommended)

pip install pointprocess

Supported platforms:

• Linux (x86_64) - Wheels distributed via PyPI
• Windows (x86_64) - Wheels distributed via PyPI
• macOS (Apple Silicon) - Wheels distributed via PyPI
• Python 3.9–3.13

Development Setup

All development work uses nox for consistency across platforms. First install system dependencies:

macOS (Homebrew):

brew install cmake boost eigen

Linux (Ubuntu/Debian):

sudo apt-get install -y cmake libboost-all-dev libeigen3-dev

Linux (Fedora/RHEL):

sudo dnf install -y cmake boost-devel eigen3-devel

Windows (Chocolatey):

choco install cmake boost-msvc-14.3 eigen

Then clone and use nox:

git clone https://github.com/andreabonvini/pointprocess.git
cd pointprocess
pipx install nox
nox

Common Development Tasks

All tasks use nox (no more bash scripts):

nox -s dev # Set up development environment
nox -s build # Build C++ extension
nox -s test# Run test suite
nox -s lint # Code quality checks (clang-format)
nox -s coverage # Generate coverage report
nox -s docs # Build Sphinx documentation
nox -s clean # Clean build artifacts

Documentation

Full documentation available at pointprocess.readthedocs.io

Quick Start

Basic Usage

importnumpyasnpimportmatplotlib.pyplotaspltfrompointprocessimport (
compute_single_regression,
compute_full_regression,
compute_spectral_analysis,
Distributions,
)
# Load RR interval data (time between heartbeats in seconds)rr=np.load("events.npy")
events=rr[75:301]
# Plot RR intervalsplt.plot(events[1:], 1000*np.diff(events), "b")
plt.xlabel("Time [s]")
plt.ylabel("RR [ms]")
plt.show()

Single Regression

Fit a point process model to a fixed window of data:

result=compute_single_regression(
events=events,
ar_order=9,
has_theta0=True,
right_censoring=False,
alpha=0.02,
distribution=Distributions.InverseGaussian,
max_iter=10000
)
# Access resultsprint(f"AR coefficients (θ_p): {result.thetap}")
print(f"Intercept (θ_0): {result.theta0}")
print(f"Shape parameter (κ): {result.kappa}")
print(f"Log-likelihood: {result.likelihood}")
print(f"Mean interval: {result.mean_interval}")

Spectral Analysis

# Compute power spectral density from model parametersanalysis=compute_spectral_analysis(
thetap=result.thetap,
mean_interval=result.mean_interval,
variance=result.sigma**2
)
# Plot power spectral densityplt.figure(figsize=(10, 6))
plt.plot(analysis.frequencies, analysis.powers, "k", linewidth=0.8)
forpoleinanalysis.poles:
plt.axvline(pole.frequency, color="r", linestyle="--", alpha=0.3)
plt.xlabel("Frequency [Hz]")
plt.ylabel("Power [ms²/Hz]")
plt.xlim(0, 0.5)
plt.show()

Full Regression (Time-Varying Analysis)

# Fit model across time with sliding windowresult_full=compute_full_regression(
events=rr,
window_length=60.0, # 60 second windowdelta=0.005, # 5 ms step sizear_order=9,
has_theta0=True,
right_censoring=True,
alpha=0.02,
distribution=Distributions.InverseGaussian,
max_iter=1000
)
# Convert to dictionary for easier accessd=result_full.to_dict()
# Plot time-varying meanplt.figure(figsize=(12, 4))
plt.plot(d["Time"], d["Mu"], "b", linewidth=0.5, label="μ(t)")
plt.xlabel("Time [s]")
plt.ylabel("Mean Interval [s]")
plt.legend()
plt.show()

For complete examples with visualizations, see the Jupyter Notebook in examples/.

Contributing

We welcome contributions! Please:

1. Fork the repository
2. Create a feature branch
3. Make your changes
4. Run tests: nox -s test
5. Submit a pull request

License

MIT License - See LICENSE file for details.

Citation

If you use this library in your research, please cite:

@software{pointprocess2026,
author = {Bonvini, Andrea},
title = {Point Process: Heart Rate Variability Analysis Library},
url = {https://github.com/andreabonvini/pointprocess},
year = {2026}
}