Model Prior Choice and Multiplicity Correction in Bayesian Model and Variable Selection

• Activity Number: 327
• Type: Topic Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Melanie Ann Wilson*+ and Merlise Clyde and Edwin Iversen
• Companies: Duke University and Duke University and Duke University
• Keywords: Bayesian Model Uncertainty ; Model Selection ; Consistency ; Model Space Priors ; Multiplicity Correction ; Variable Selection

Abstract

Much of the recent Bayesian model uncertainty literature has focused on defining prior distributions in an objective manner, providing conditions under which Bayes factors lead to the correct model selection, particularly in the situation where the number of variables (p) increases with the sample size (n), a frequent occurrence in the "-omics" era. In this context we characterize commonly used prior distributions on the model space and investigate their implicit multiplicity correction properties in the extreme case of including an increasing number of redundant covariates and under arbitrary design matrices. We provide conditions on the asymptotic (in n and p) behavior of the prior odds of the global hypothesis of association required to achieve consistent model selection of the null model in terms of its posterior model probability and in terms of posterior inclusion probabilities.