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The choice of model class is fundamental in statistical learning and systemidentification, no matter whether the class is derived from physical principlesor is a generic black-box. We develop a method to evaluate the specified modelclass by assessing its capability of reproducing data that is similar to theobserved data record. This model check is based on the information-theoreticproperties of models viewed as data generators and is applicable to e.g.sequential data and nonlinear dynamical models. The method can be understood asa specific two-sided posterior predictive test. We apply theinformation-theoretic model check to both synthetic and real data and compareit with a classical whiteness test.

How consistent is my model with the data? Information-Theoretic Model Check