Bayesian inference of scaled versus fractional Brownian motion

TL;DR

This paper introduces a Bayesian inference method for distinguishing scaled Brownian motion from fractional Brownian motion, effectively estimating parameters and selecting models even with measurement noise and limited data.

Contribution

It develops an optimal Bayesian inference scheme for scaled and fractional Brownian motion, incorporating measurement noise and demonstrating high accuracy with synthetic data.

Findings

Accurately resolves true model and parameters with a few hundred data points.

Optimal inference achieved when using the same prior as data generation.

Comparison shows robustness even with different priors.

Abstract

We present a Bayesian inference scheme for scaled Brownian motion, and investigate its performance on synthetic data for parameter estimation and model selection in a combined inference with fractional Brownian motion. We include the possibility of measurement noise in both models. We find that for trajectories of a few hundred time points the procedure is able to resolve well the true model and parameters. Using the prior of the synthetic data generation process also for the inference, the approach is optimal based on decision theory. We include a comparison with inference using a prior different from the data generating one.