The Annals of Statistics

Posterior propriety and admissibility of hyperpriors in normal hierarchical models

James O. Berger, William Strawderman, and Dejun Tang

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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.

Article information

Ann. Statist., Volume 33, Number 2 (2005), 606-646.

First available in Project Euclid: 26 May 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62C15: Admissibility
Secondary: 62F15: Bayesian inference

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


Berger, James O.; Strawderman, William; Tang, Dejun. Posterior propriety and admissibility of hyperpriors in normal hierarchical models. Ann. Statist. 33 (2005), no. 2, 606--646. doi:10.1214/009053605000000075.

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