The Intrinsic Bayes Factor for Model Selection and Prediction

TLDR

Bayesian model selection often cannot use noninformative priors, leading Bayesians to rely on proper priors or crude Bayes factor approximations. The authors introduce the intrinsic Bayes factor, a fully automatic criterion that uses only standard noninformative priors. The intrinsic Bayes factor applies to nested or nonnested models and supports multiple model comparison and prediction. The work also proposes a general definition of a reference prior for model comparison. Keywords: asymptotic Bayes factors, hypothesis testing, noninformative prior, posterior probability, training sample.

Abstract

Abstract In the Bayesian approach to model selection or hypothesis testing with models or hypotheses of differing dimensions, it is typically not possible to utilize standard noninformative (or default) prior distributions. This has led Bayesians to use conventional proper prior distributions or crude approximations to Bayes factors. In this article we introduce a new criterion called the intrinsic Bayes factor, which is fully automatic in the sense of requiring only standard noninformative priors for its computation and yet seems to correspond to very reasonable actual Bayes factors. The criterion can be used for nested or nonnested models and for multiple model comparison and prediction. From another perspective, the development suggests a general definition of a "reference prior" for model comparison. Key Words: Asymptotic Bayes factorsHypothesis testingNoninformative priorPosterior probabilityTraining sample