Posterior propriety and admissibility of hyperpriors in normal hierarchical models

James O. Berger, William Strawderman, Dejun Tang

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)606-646
Number of pages41
JournalAnnals of Statistics
Issue number2
StatePublished - Apr 2005

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Covariance matrix
  • Frequentist risk
  • Markov chain Monte Carlo
  • Objective priors
  • Posterior impropriety
  • Quadratic loss


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