Bayes Not Bust! Why Simplicity Is No Problem for Bayesians

Abstract
The advent of formal definitions of the simplicity of a theory has important implications for model selection. But what is the best way to define simplicity? Forster and Sober ([1994]) advocate the use of Akaike's Information Criterion (AIC), a non-Bayesian formalisation of the notion of simplicity. This forms an important part of their wider attack on Bayesianism in the philosophy of science. We defend a Bayesian alternative: the simplicity of a theory is to be characterised in terms of Wallace's Minimum Message Length (MML). We show that AIC is inadequate for many statistical problems where MML performs well. Whereas MML is always defined, AIC can be undefined. Whereas MML is not known ever to be statistically inconsistent, AIC can be. Even when defined and consistent, AIC performs worse than MML on small sample sizes. MML is statistically invariant under 1-to-1 re-parametrisation, thus avoiding a common criticism of Bayesian approaches. We also show that MML provides answers to many of Forster's objections to Bayesianism. Hence an important part of the attack on Bayesianism fails
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References found in this work BETA
MR Forster (1999). Model Selection in Science: The Problem of Language Variance. British Journal for the Philosophy of Science 50 (1):83-102.
Citations of this work BETA
Jan Sprenger (2013). The Role of Bayesian Philosophy Within Bayesian Model Selection. European Journal for Philosophy of Science 3 (1):101-114.
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