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 that may serve as a goodness-of-fit, like the χ^{2} 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.