Bayesian Multiplicity Adjustment in Selection and Partitioning Problems

• Activity Number: 244
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Dan Spitzner*
• Companies: University of Virginia
• Keywords: Bayes factors ; variable selection ; clustering ; multiple testing ; non-local prior

Abstract

A multiplicity adjustment is proposed for multiple testing problems that is specified through the discrete prior, i.e., the prior model probabilities. The proposed scheme makes use of a graphical nesting structure between models to explore asymptotic consistency of model choice, with respect to simultaneous increases in sample size and dimensionality. From this viewpoint, variable selection is shown to represent an interesting balance point among multiple testing problems. Moreover, the scheme identifies performance improvements over standard variable selection priors, such as beta-binomial priors, and establishes asymptotic consistence in "ultra-high" dimensions. Criteria for asymptotic consistency in partition-based clustering problems are also explored, and point to a new prior specification that induces good performance. Issues of interpretation with regard to the discrete prior's representation of subjective knowledge are also discussed.