Kolmogorov´s structure function for probability models

This work was inspired by the paper of Vereshchagin and Vitanyi, where Kolmogorov´s unpublished work on his structure function and the associated minimal sufficient statistics decomposition in the algorithmic theory of information is studied. The extension of Kolmogorov´s great ideas to probability model classes turns out to add a new chapter to the MDL theory, which also provides an alternative approach to Shannon´s rate-distortion theory.