  The Bayesian data analysis framework has been proven to be a systematic and
effective method of parameter inference and model selection for stochastic
processes. In this work we introduce an information content model check which
may serve as a goodness-of-fit, like the chi-square procedure, to complement
conventional Bayesian analysis. We demonstrate this extended Bayesian framework
on a system of Langevin equations, where coordinate dependent mobilities and
measurement noise hinder the normal mean squared displacement approach.
