Discussion on Kolmogorov Complexity and Statistical Analysis

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 Vitányi [6], Rissanen [3], Wallace and Dowe [7] 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.