Statistics Papers

Document Type

Journal Article

Date of this Version

4-1-2008

Publication Source

Journal of Statistical Planning and Inference

Volume

138

Issue

4

Start Page

888

Last Page

900

DOI

10.1016/j.jspi.2007.02.011

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. Calibration and Empirical Bayes variable selection. Biometrika 87(4), 731–747] to improve on these fixed selection criteria. In this paper, 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 for which fully Bayes selection and estimation methods are obtained. Analytical and simulation comparisons with empirical Bayes counterparts are studied.

Copyright/Permission Statement

© 2008. This manuscript version is made available under the CC-BY-NC-ND 4.0 license.

Keywords

hyperparameter uncertainty, model selection, objective Bayes

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Date Posted: 27 November 2017

This document has been peer reviewed.