On the Bayesian “occam Factors” Argument for Occam’s Razor

This paper discusses some of the problematic aspects of the Bayesian first-principles “proof” of Occam’s razor which involves Occam factors. Although it is true that the posterior for a model is reduced due to Occam factors if that model is capable of expressing many functions, the phenomenon need not have anything to do with Occam’s razor. This paper shows this by i) performing reductio ad absurdum on the argument that the Occam factors effect implies Occam’s razor; ii) presenting an alternative Bayesian approach which explicitly does not result in Occam’s razor; and finally iii) disentangling the underlying problem with viewing the Occam factors argument as a proof or “automatic embodiment” of Occam’s razor.