Model selection and testing by the MDL principle

Abstract

This chapter is an outline of the latest developments in the MDL theory as applied to the selection and testing of statistical models. Finding the number of parameters is done by a criterion defined by an MDL based universal model, while the corresponding optimally quantized real valued parameters are determined by the so-called structure function following Kolmogorov's idea in the algorithmic theory of complexity. Such models are optimally distinguishable, and they can be tested also in an optimal manner, which differs drastically from the Neyman-Pearson testing theory. © 2009 Springer US.