Bayesian model selection with fractional Brownian motion

TL;DR

This paper develops a Bayesian framework for selecting models and estimating parameters of fractional Brownian motion with noise, demonstrating its effectiveness on simulated and real biological data, and introducing a goodness-of-fit test.

Contribution

It introduces a Bayesian approach for model selection and parameter estimation in fractional Brownian motion with noise, including a goodness-of-fit test for real data analysis.

Findings

Accurate parameter estimates on artificial data

Preference for simpler models with finite trajectories

Goodness-of-fit test detects discrepancies in biological data

Abstract

We implement Bayesian model selection and parameter estimation for the case of fractional Brownian motion with measurement noise and a constant drift. The approach is tested on artificial trajectories and shown to make estimates that match well with the underlying true parameters, while for model selection the approach has a preference for simple models when the trajectories are finite. The approach is applied to observed trajectories of vesicles diffusing in Chinese hamster ovary cells. Here it is supplemented with a goodness-of-fit test, which is able to reveal statistical discrepancies between the observed trajectories and model predictions.