The role of Bayesian philosophy within Bayesian model selection

Jan Sprenger

doi:10.1007/s13194-012-0059-5

Abstract

Abstract Bayesian model selection has frequently been the focus of philosophical inquiry (e.g., Forster, Br J Philos Sci 46:399–424, 1995; Bandyopadhyay and Boik, Philos Sci 66:S390–S402, 1999; Dowe et al., Br J Philos Sci 58:709–754, 2007). This paper argues that Bayesian model selection procedures are very diverse in their inferential target and their justification, and substantiates this claim by means of case studies on three selected procedures: MML, BIC and DIC. Hence, there is no tight link between Bayesian model selection and Bayesian philosophy. Consequently, arguments for or against Bayesian reasoning based on properties of Bayesian model selection procedures should be treated with great caution.

Highlights

Model selection is a relatively young subfield of statistics that compares statistical models on the basis of their structural properties and their fit to the data
This paper explores the extent to which Bayesian model selection procedures are anchored within Bayesian philosophy, and in particular their philosophical justification
What do Bayesian model selection procedures teach us about Bayesian philosophy of science? Their explicitly Bayesian formalism suggests that they are supported by a full-fledged Bayesian philosophy of inference

Summary

Introduction

Model selection is a relatively young subfield of statistics that compares statistical models on the basis of their structural properties and their fit to the data. Instead of conforming to the subjective Bayesian rationale, 2This is different from objective Bayesian inference where the two basic constraints of Bayesian inference—a coherent prior distribution and conditionalization on incoming evidence—are supplemented by further requirements that narrow down the set of rational degrees of belief, often up to uniqueness. They are hybrid procedures: they do not primarily aim at an accurate representation of subjective uncertainty, but use the Bayesian calculus as a convenient mathematical tool for diverse epistemological goals. This has, as I shall argue in the conclusions, substantial repercussions on some bold methodological claims regarding Bayesian reasoning that are made in the literature

MML and the conditionality principle

Bayesianism without model priors

Estimating effective complexity

Conclusions