Some Recent Developments in Bayesian Model Selection

James O. Berger
Duke University and SAMSI

Abstract
We review two fairly recent developments in Bayesian model selection

  1. A generalization of BIC has recently been developed, for contexts common in the social sciences, that appropriately assesses the dimension of a model and the effective sample size for each parameter in a model. The generalization allows for the model dimension to grow with the sample size.
  1. When the space of models is large, Search Strategies need to be carefully developed for exploration of the space. One successful strategy in variable selection is to perform a stochastic search that (roughly) adds or removes variables based on their current estimated posterior inclusion probabilities. This approach, and related diagnostics, will be illustrated. An interesting phenomenon that seems to be frequently encountered is that no model receives significant posterior probability, so that the meaning of model selection and the questions we pose concerning models may need to be reconsidered.