Bayesian inference with information content model check for Langevin equations

TL;DR

This paper introduces an information content model check to enhance Bayesian inference for Langevin equations, providing a goodness-of-fit measure that addresses challenges like coordinate-dependent mobilities and measurement noise.

Contribution

It presents a novel information content model check as a complement to Bayesian analysis for stochastic processes, specifically applied to Langevin equations.

Findings

Effective goodness-of-fit measure for Langevin models

Addresses measurement noise and coordinate-dependent mobilities

Enhances Bayesian inference reliability

Abstract

The Bayesian data analysis framework has been proven to be a systematic and effective method of parameter inference and model selection for stochastic processes. In this work we introduce an information content model check which may serve as a goodness-of-fit, like the chi-square procedure, to complement conventional Bayesian analysis. We demonstrate this extended Bayesian framework on a system of Langevin equations, where coordinate dependent mobilities and measurement noise hinder the normal mean squared displacement approach.