Bayesian inference of scaled versus fractional Brownian motion

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.

Automated summary

We present a Bayesian inference scheme for scaled Brownian motion and investigate its performance on parameter estimation and model selection in a combined inference with fractional Brownian motion. The results show that the procedure is able to accurately resolve the true model and parameters for trajectories of a few hundred time points, and the approach using the prior of the synthetic data generation process is optimal based on decision theory.