Posterior propriety and admissibility of hyperpriors in normal hierarchical models
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2005
 DOI:
 10.48550/arXiv.math/0505605
 arXiv:
 arXiv:math/0505605
 Bibcode:
 2005math......5605B
 Keywords:

 Mathematics  Statistics;
 62C15 (Primary) 62F15 (Secondary)
 EPrint:
 Published at http://dx.doi.org/10.1214/009053605000000075 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)