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

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