Posterior propriety and admissibility of hyperpriors in normal hierarchical models

Details Posterior propriety and admissibility of hyperpriors in normal hierarchical models Posterior propriety and admissibility of hyperpriors in normal hierarchical models

2005-05-27

arxiv.org/abs/math/0505605v1

Annals of Statistics 2005, Vol. 33, No. 2, 606-646

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053605000000075 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053605000000075

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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