Bayes Rules in Finite Models
Stefan Arnborg, Gunnar Sjödin · 2000
. Of the many justifications of Bayesianism, most imply some assumption that is not very compelling, like the differentiability or continuity of some auxiliary function. We show how such assumptions can be replaced by weaker assumptions for finite domains. The new assumptions are a non-informative refinement principle and a concept of information independence. These assumptions are weaker than those used in alternative justifications, which is shown by their inadequacy for infinite domains. They are also more compelling. 1 Introduction The normative claim of Bayesianism is that every type of uncertainty should be described as probability. Bayesianism has been quite controversial in both the statistics and the uncertainty management communities. It developed as subjective Bayesianism, in [5, 11]. Recently, the information based family of justifications, initiated in [3] and continued in [1] have been discussed in [12, 6, 13]. We will try to find assumptions that are strong enough to s...