Posterior propriety and admissibility of hyperpriors in normal hierarchical models

By James O. Berger, William E. Strawderman, Dejun Tang. 2005

53 citations recorded by the source corpus.

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.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4276196f7a2d72c05c3f21bc2518257815b4b253

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Objective priors for the bivariate normal model (2008, background): “Berger, Strawderman and Tang [4] gave a Metropolis–Hastings algorithm to generate from (σ1, σ2, ρ |X) based on the prior πRλ.”
The case for objective Bayesian analysis (2006, background): “Berger et al. (2005a), which is under preparation, will be presenting such unique recommended objective priors.”