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April 2005 Posterior propriety and admissibility of hyperpriors in normal hierarchical models
James O. Berger, William Strawderman, Dejun Tang
Ann. Statist. 33(2): 606-646 (April 2005). DOI: 10.1214/009053605000000075

Abstract

Hierarchical modeling is wonderful and here to stay, but hyperparameter priors are often chosen in a casual fashion. Unfortunately, as the number of hyperparameters grows, the effects of casual choices can multiply, leading to considerably inferior performance. As an extreme, but not uncommon, example use of the wrong hyperparameter priors can even lead to impropriety of the posterior.

For exchangeable hierarchical multivariate normal models, we first determine when a standard class of hierarchical priors results in proper or improper posteriors. We next determine which elements of this class lead to admissible estimators of the mean under quadratic loss; such considerations provide one useful guideline for choice among hierarchical priors. Finally, computational issues with the resulting posterior distributions are addressed.

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James O. Berger. William Strawderman. Dejun Tang. "Posterior propriety and admissibility of hyperpriors in normal hierarchical models." Ann. Statist. 33 (2) 606 - 646, April 2005. https://doi.org/10.1214/009053605000000075

Information

Published: April 2005
First available in Project Euclid: 26 May 2005

zbMATH: 1068.62005
MathSciNet: MR2163154
Digital Object Identifier: 10.1214/009053605000000075

Subjects:
Primary: 62C15
Secondary: 62F15

Keywords: Covariance matrix , frequentist risk , Markov chain Monte Carlo , objective priors , posterior impropriety , quadratic loss

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 2 • April 2005
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