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Berger, James O.; Strawderman, William; Tang, Dejun

Posterior propriety and admissibiity of hyperpriors in normal hierarchical models. (English) Zbl 1068.62005

Ann. Stat. 33, No. 2, 606-646 (2005).
Summary: 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.

Cited in 23 Documents

MSC:

62C15 Admissibility in statistical decision theory
62H10 Multivariate distribution of statistics
62H12 Estimation in multivariate analysis
62F15 Bayesian inference

Keywords:

covariance matrix; quadratic loss; frequentist risk; posterior impropriety; objective priors; Markov chain Monte Carlo
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\textit{J. O. Berger} et al., Ann. Stat. 33, No. 2, 606--646 (2005; Zbl 1068.62005)
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