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 \(\mathbf{X}_t\) on a domain \(\Omega\subset\mathbb{R}^d\), indexed over \(t\in\mathbb{R}_+\),
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,
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
Installation and Development¶
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:
Documentation¶
A walk-through for solving a simple inference problem with SPIN is given in the Tutorial. We further provide runnable examples for different use-cases in our Github repository. For more information regarding the implementation of SPIN, we refer to the API reference.
Acknowledgement and License¶
SPIN is being developed in the research group Uncertainty Quantification at KIT. Large portions of SPIN are based on the hIPPYlib software library for large-scale (Bayesian) inverse problems. hIPPYlib, in turn, uses FEniCS for finite element computations. SPIN is distributed as free software under the MIT License.