Fast Bayesian inference of optical trap stiffness and particle diffusion

TL;DR

This paper introduces fast Bayesian methods for accurately estimating optical trap stiffness and particle diffusion from experimental data, outperforming traditional non-Bayesian approaches.

Contribution

It develops exact likelihood-based Bayesian inference techniques for the Ornstein-Uhlenbeck process, enabling rapid and precise parameter estimation without Monte Carlo sampling.

Findings

Bayesian methods outperform non-Bayesian fitting in accuracy.

The approach provides simple maximum a posteriori estimates.

Methods are computationally efficient and suitable for experimental data.

Abstract

Bayesian inference provides a principled way of estimating the parameters of a stochastic process that is observed discretely in time. The overdamped Brownian motion of a particle confined in an optical trap is generally modelled by the Ornstein-Uhlenbeck process and can be observed directly in experiment. Here we present Bayesian methods for inferring the parameters of this process, the trap stiffness and the particle diffusion coefficient, that use exact likelihoods and sufficient statistics to arrive at simple expressions for the maximum a posteriori estimates. This obviates the need for Monte Carlo sampling and yields methods that are both fast and accurate. We apply these to experimental data and demonstrate their advantage over commonly used non-Bayesian fitting methods.