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

import numpy as np
import matplotlib.pyplot as plt
from pointprocess import (
    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 intervals
plt.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 results
print(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 parameters
analysis = compute_spectral_analysis(
    thetap=result.thetap,
    mean_interval=result.mean_interval,
    variance=result.sigma ** 2
)

# Plot power spectral density
plt.figure(figsize=(10, 6))
plt.plot(analysis.frequencies, analysis.powers, "k", linewidth=0.8)
for pole in analysis.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 window
result_full = compute_full_regression(
    events=rr,
    window_length=60.0,      # 60 second window
    delta=0.005,             # 5 ms step size
    ar_order=9,
    has_theta0=True,
    right_censoring=True,
    alpha=0.02,
    distribution=Distributions.InverseGaussian,
    max_iter=1000
)

# Convert to dictionary for easier access
d = result_full.to_dict()

# Plot time-varying mean
plt.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}
}