Bayesian inference of scaled versus fractional Brownian motion

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.

22 pages, 12 figures, IOP LaTeX, minor revisions

References in corpus (3)

• Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
• Continuous Time Random Walks (CTRWs): Simulation of continuous trajectories
• Bayesian inference with information content model check for Langevin equations

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