Discussion of the Papers by Rissanen, and by Wallace and Dowe

Commenting on the papers by Dr Rissanen and Professors Wallace and Dowe is a daunting sort of pleasure. Superficially, the papers are not closely related: Dr Rissanen has focused on the Shtarkov optimality criterion in a minimum description length (MDL) context giving some new implications from normalization (see his equation (1)) for model selection and hypothesis testing. By contrast, Wallace and Dowe have given a first, and welcome, effort to axiomatize a setting in which it is reasonable to hope that the algorithmic complexity approaches of Kolmogorov and Solomonoff—streams one and two, using UTMs—may coincide with the Shannon theory approaches—stream three in its minimum message length (MML) and MDL versions. Despite these differences, there are several senses in which these two papers are closely related.