The intrinsic Bayes factor for model selection and prediction

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.