Reference Prior in High-Dimensional Exponential Families

• Activity Number: 349
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Bertrand Clarke and Subhashis Ghoshal*+
• Companies: University of Miami and North Carolina State University
• Keywords: Reference prior ; high dimension ; posterior normality ; Jeffreys prior ; asymptotic expansion

Abstract

Reference prior is a key concept in objective Bayesian analysis, which results from an asymptotic maximization of the expected relative entropy distance between the posterior and the prior. Posterior asymptotic normality plays a key role in the asymptotic expansion. In the absence of a nuisance parameter, the Jeffreys prior turns out to be the reference prior. In this talk, we investigate to what extent, this conclusion remains valid when the dimension of the parameter space in an exponential family increases to infinity with the sample size. We quantify the allowable rate of growth of the dimension for the asymptotic expansion of the expected relative entropy to hold. The required growth condition depends on various factors in the model and the prior. We specifically discuss two examples --- independent normal location model and the multinomial model.