A Consistency Result for Bayesian Model Selection Using Nonlocal Priors

• 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): Valen Johnson*+
• Companies: MD Anderson Cancer Center
• Keywords: Bayes factor ; intrinsic Bayes factor ; objective Bayes ; default prior

Abstract

Abstract: Let Y denote an n x 1 random vector, X an n x q matrix of real numbers, and b a q x 1 regression vector. This talk addresses the selection of the non-zero components of b when it is assumed that

Y ~ N(Xb,sigma^2 I)

and q is O(n). Model selection is based on the calculation of posterior model probabilities using non-local prior densities on the regression coefficients for each possible model. The non-local prior densities used for model definition are obtained as products of independent normal moment priors and are called pMOM prior densities. Under mild conditions on the matrix X'X, I demonstrate that the use of these priors guarantees that the posterior probability of the true model approaches 1 as n becomes large.