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.