Abstract #300492

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JSM 2003 Abstract #300492
Activity Number: 173
Type: Contributed
Date/Time: Monday, August 4, 2003 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Stat. Sciences
Abstract - #300492
Title: Variable Selection: Empirical Bayes vs. Fully Bayes
Author(s): Wen (Jessica) Cui*+ and Edward I. George
Companies: Southwest Texas State University and University of Pennsylvania
Address: 15850 Garrison Circle, Austin, TX, 78717-3005,
Keywords: hierarchical Bayes ; hyperparameters ; model selection ; prior distributions ; risk
Abstract:

For the problem of variable selection for the normal linear model, fixed penalty selection criteria such as AIC, Cp, BIC and RIC correspond to the posterior modes of a hierarchical Bayes model for various fixed hyperparameter settings. Adaptive selection criteria obtained by empirical Bayes estimation of the hyperparameters have been shown by George and Foster (2000) to improve on these fixed selection criteria. We study the potential of alternative fully Bayes methods, which instead margin out the hyperparameters with respect to prior distributions. Several structured prior formulations are considered, and a variety of fully Bayes selection and estimation methods are obtained. Extensive comparisons with their empirical Bayes counterparts suggest that the empirical Bayes methods perform extremely well in spite of their known inadmissibility.

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