A note on posterior expansions

• Activity Number: 536
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Chiu-Hsing Weng*+
• Companies: National Chengchi University
• Keywords: Laplace method ; posterior distribution ; Stein's identity

Abstract

Johnson (1970) obtained expansions for marginal posterior distributions by Taylor expansions. Here the posterior expansion is expressed in terms of the likelihood and the prior together with their derivatives. Recently Weng (2010) applies a version of Stein's identity to obtain a Bayesian Edgeworth expansion, where the expansion is expressed by posterior moments. It is of interest to examine the relation between the two expansions. The present paper first derives approximations for posterior moments in terms of the likelihood and the prior, and then shows that by substituting these approximations into the Edgeworth series it leads to Johnson's result. We also study approximations to the predictive density and conduct a simulation study to assess its accuracy.