SPIN: Stochastic Process INference

SPIN is a Python package for the non-parametric Bayesian inference of the parameter functions of autonomous diffusion processes. It can be used to infer the drift function $\mathbf{b}: \Omega\to\mathbb{R}^d$ and (squared) diffusion function $\mathbf{\Sigma}:\Omega\to\mathbb{R}^{d\times d}$ from trajectory data of an underlying process $\mathbf{X}$ on a domain $\Omega\subset\mathbb{R}^d$, indexed over $t\in\mathbb{R} _+ $,

$$ d\mathbf{X}_t = \mathbf{b}(\mathbf{X}_t) dt + \sqrt{\mathbf{\Sigma}(\mathbf{X}_t)} d\mathbf{W}_t,\quad \mathbf{X}(t=0)=\mathbf{X}_0\ a.s. $$

Under the hood, SPIN employs a PDE-based inference method, based on the Kolmogorov equations governing the stochastic process under consideration. For more information on the underlying theory, we refer to the accompanying publication,

Non-parametric Inference for Diffusion Processes: A Computational Approach via Bayesian Inversion for PDEs

Key Features

• Non-parametric inference of drift and diffusion functions
• Works with stationary and time-dependent trajectory data
• PDE computations based on the finite element method
• Evaluation of the maximum a-posteriori estimate and Laplace approximation
• Generic and robust implementation, based on hIPPYlib and FEniCS

Getting Started

SPIN depends on a mixture of pip and conda dependencies, which can be efficiently managed using Pixi. To set up a virtual environment in which SPIN can be run, simply execute in the project root directory:

pixi install

The documentation provides further information regarding usage, theoretical background, technical setup and API. We also provide runnable notebooks under examples.