Extended Bayesian Information Criteria for Model Selection with Large Model Spaces

Abstract

The ordinary Bayes information criterion is too liberal for model selection when the model space is large. In this talk, we re-examine the Bayesian paradigm for model selection and present an extended family of Bayes information criteria. The new criteria take into account both the number of unknown parameters and the complexity of the model space. Their consistency is established, particularly allowing the number of covariates to increase to infinity with the sample size. Their performance in various situations is evaluated by simulation studies. It is demonstrated that the extended Bayes information criteria incur a small loss in the positive selection rate but tightly control the false discovery rate, a desirable property in many applications.B The extended Bayes information criteria are extremely useful for variable selection in problems with a moderate sample size but a huge number of covariates, especially in genome-wide association studies, which are now a hot area in genetics research.