intensify 0.2.0

A modern Python point process library with deep Hawkes specialization, dual-domain interfaces for quantitative finance and computational neuroscience.

intensify

A modern Python point process library with deep Hawkes specialization — built for quantitative finance and computational neuroscience, tested on real spike-train recordings, and JAX-accelerated end-to-end.

pip install intensify

Quickstart

import numpy as np
import intensify as its

# Simulate some event times
events = np.array([0.1, 0.5, 1.2, 1.8, 2.3, 3.1, 3.7, 4.4])
T = 5.0

# Fit a univariate Hawkes model with exponential kernel
model = its.Hawkes(mu=0.5, kernel=its.ExponentialKernel(alpha=0.3, beta=1.5))
result = model.fit(events, T=T)

print(f"Branching ratio: {result.branching_ratio_:.3f}")
print(f"Log-likelihood:  {result.log_likelihood:.3f}")
print(f"Fitted params:   {result.flat_params()}")

# Visualize fitted intensity and diagnostics
its.plot_intensity(result)

Features

• Core processes: homogeneous / inhomogeneous Poisson, Cox (Log-Gaussian, Shot-Noise), Hawkes (univariate, multivariate, marked, nonlinear / inhibitory).
• Kernel family: Exponential, Sum-of-Exponentials, Power-Law, Approximate Power-Law (Bacry–Muzy), Nonparametric (piecewise-constant). Every kernel is supported in every MLE path.
• Inference: MLE via JAX autodiff with an O(N) recursive likelihood for exponential-family kernels; EM for mixtures; online (streaming) updates; Bayesian MCMC (experimental, numpyro backend).
• Diagnostics: time-rescaling theorem (KS + QQ on inter-compensator increments — the mathematically correct form), AIC/BIC, residual intensity.
• Simulation: Ogata thinning (general) and cluster/branching (Galton–Watson).
• Stationarity enforcement: projected gradient for multivariate Hawkes; spectral radius of the kernel-norm matrix reported on every multivariate FitResult.
• Backends: JAX (JIT + autodiff, default) with a NumPy fallback. Switch at runtime with its.set_backend("numpy").

Why intensify?

intensify and tick solve partly overlapping problems. Pick the right tool:

Capability	intensify	tick
Joint MLE of (μ, α, β) — fits the decay for you	✓	— (decay must be supplied)
MLE for power-law, approx-power-law, nonparametric kernels	✓	—
Marked Hawkes fit with any kernel	✓	—
Nonlinear (softplus / sigmoid / relu) Hawkes, signed kernels	✓	—
Multivariate stationarity enforcement (projected gradient)	✓	—
Time-rescaling test on inter-compensator increments	✓	✓
Python 3.10 – 3.14 support, pure-Python install	✓	3.8 only, C++ build
Microsecond fits for exp kernels with known decay	still improving	✓ (C++)

Concrete numbers, head-to-head: docs/benchmarks.md. Short version, on the apples-to-apples problem (decay-given, the case tick can solve at all): univariate fit is 2.6 ms vs tick 1 ms; multivariate mv_exp_5d is 17 ms vs tick 2 ms — and intensify is more accurate (parameter RMSE 0.041 vs 0.052). For kernels tick doesn't ship (power-law, nonparametric, signed, marked, nonlinear) intensify is the only option. pyhawkes is no longer usable — its transitive deps depend on APIs removed from SciPy 1.0 in 2017.

Documentation

Full docs: https://hillmatt7.github.io/intensify

• Getting started
• User guide: inference, kernels, simulation, diagnostics
• Domain guides: quantitative finance, computational neuroscience
• API reference
• Tutorials (Jupyter notebooks)

Citation

If you use intensify in academic work, please cite it:

@software{intensify,
  author = {Hill, Matthew},
  title  = {intensify: A modern Python point process library with deep Hawkes specialization},
  year   = {2026},
  url    = {https://github.com/hillmatt7/intensify}
}

See CITATION.cff for the machine-readable form.

Contributing & changes

• Contributing guide
• Changelog
• Open issues

License

MIT — see LICENSE.