NML, Bayes and true distributions: A comment on Karabatsos and Walker (2006)

摘要: Abstract We review the normalized maximum likelihood (NML) criterion for selecting among competing models. NML is generally justified on information-theoretic grounds, via principle of minimum description length (MDL), in a derivation that “does not assume existence true, data-generating distribution”. Since this “agnostic” claim has been source some recent confusion psychological literature, we explain detail what meant by statement. In doing so discuss work presented [Karabatsos, G., & Walker, S. G. (2006). On and Bayesian decision theory. Journal Mathematical Psychology, 50, 517–520], who propose an alternative decision-theoretic characterization NML, which leads them to conclude agnosticity meaningless. KW derivation, one part (the term) arises from placing Dirichlet process prior over possible distributions, other complexity folded into loss function. Whereas original derivations term naturally, KW derivation its mathematical form taken granted explained any further. argue reason, KW characterization incomplete; relatedly, question relevance their main conclusion about does follow.