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The Bayesian data analysis framework has been proven to be a systematic andeffective method of parameter inference and model selection for stochasticprocesses. In this work we introduce an information content model check whichmay serve as a goodness-of-fit, like the chi-square procedure, to complementconventional Bayesian analysis. We demonstrate this extended Bayesian frameworkon a system of Langevin equations, where coordinate dependent mobilities andmeasurement noise hinder the normal mean squared displacement approach.

Bayesian inference with information content model check for Langevin equations