# Statistical Tests for Force Inference in Heterogeneous Environments

## TL;DR

This paper introduces a Bayesian inference method to detect and estimate forces in heterogeneous environments from stochastic trajectories, accounting for spurious forces due to spatially varying diffusivity, and validates it analytically, numerically, and experimentally.

## Contribution

It presents a novel Bayesian approach for force inference that marginalizes over spurious forces and incorporates a statistical test, implemented in open-source software.

## Key findings

- Method reliably detects forces in heterogeneous environments.
- Analytical and numerical validation shows high accuracy.
- Tested successfully on experimental biomolecule trajectory data.

## Abstract

We devise a method to detect and estimate forces in a heterogeneous environment based on experimentally recorded stochastic trajectories. In particular, we focus on systems modeled by the heterogeneous overdamped Langevin equation. Here, the observed drift includes a "spurious" force term when the diffusivity varies in space. We show how Bayesian inference can be leveraged to reliably infer forces by taking into account such spurious forces of unknown amplitude as well as experimental sources of error. The method is based on marginalizing the force posterior over all possible spurious force contributions. The approach is combined with a Bayes factor statistical test for the presence of forces. The performance of our method is investigated analytically, numerically and tested on experimental data sets. The main results are obtained in a closed form allowing for direct exploration of their properties and fast computation. The method is incorporated into TRamWAy, an open-source software platform for automated analysis of biomolecule trajectories.