Discussion on Kolmogorov complexity and statistical analysis

Abstract

The question why and how probability theory can be applied to the real-world phenomena has been discussed for several centuries. When the algorithmic information theory was created, it became possible to discuss these problems in a more specific way. In particular, Li and Vitanyi, Rissanen, Wallace and Dowe have discussed the connection between Kolmogorov (algorithmic) complexity and minimum description length (minimum message length) principle. In this note we try to point out a few simple observations that (we believe) are worth keeping in mind while discussing these topics.