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Abstract:
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Normal hierarchical models are the workhorse of much of Bayesian analysis, yet there is uncertainty as to which objective priors to use for hyperparmeters. Formal approaches to objective Bayesian analysis, such as the Jeffreys-rule or reference prior approach, are only implementable in simple hierarchical settings. Using formal priors from non-hierarchical models in hierarchical settings can be fraught with danger. Berger, Strawderman and Tang (2005) approached the question of choice of hyperpriors in normal hierarchical models from the frequentist notion of admissibility of resulting estimators. Hyperpriors that are `on the boundary of admissibility' are sensible choices for objective priors. The admissibility (and propriety) properties of a number of priors were considered in the paper, but no overall conclusion was reached as to a specific prior to recommend, due to the difficulty in proving admissibility for the leading candidate prior. In this talk, we complete the story and propose a particular objective prior for use based on considerations of admissibility, ease of implementation (including computational considerations), and performance.
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