Title: How consistent is my model with the data? Information-Theoretic Model Check,
Abstract: 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.