JSM 2005 - Toronto

Abstract #304834

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 363
Type: Contributed
Date/Time: Wednesday, August 10, 2005 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Statistical Science
Abstract - #304834
Title: Posterior Propriety for Hierarchical Models with Log-concave Likelihoods, Including Hierarchical Generalized Linear Models
Author(s): Sarah Michalak*+ and Carl N. Morris
Companies: Los Alamos National Laboratory and Harvard University
Address: P. O. Box 1663, Los Alamos, NM, 87545, USA
Keywords: Multi-Level Model ; Generalized Linear Model ; Log-Concave Likelihood ; Hierarchical Logistic Regression ; Improper Prior ; Frequency Properties
Abstract:

Improper priors are sometimes used in Bayesian data analyses. In particular, there may be a dearth of prior information or an improper prior may be chosen because it has been shown to lead to good frequency properties for some of the estimates of interest. When using an improper prior, it is essential to determine that the resulting posterior distribution is proper. This talk presents conditions for posterior propriety for a general class of hierarchical models that includes certain hierarchical generalized linear models. We also present conditions for the existence of posterior moments of certain functions of the model parameters. Such results are essential as it is nonsensical to calculate estimates of posterior moments that do not exist. Our conditions for posterior propriety and the existence of posterior moments are easy to use: verifying whether they are satisfied in a given case does not require the evaluation of integrals or other difficult calculations. Finally, our results apply to a class of priors shown to provide good frequency properties to the resulting Level I mean estimates for important models.

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Revised March 2005