Bayesian inference for Brownian dynamics

We present a Bayesian method for inferring the potential energy experienced by a particle subject to Brownian dynamics. Assuming polynomial potentials, the best polynomial order can be determined by analytical computation of a series of Bayes factors. The coefficients can be estimated from marginal posterior distributions. The method is applicable not only for the motion of an actual Brownian particle but to many kinds of single degree-of-freedom trajectories with Gaussian noise and short, nonzero correlation times.