#### Posterior Propriety and Admissibility of
Hyperpriors in Normal Hierarchical Models

J.O. Berger, W.E. Strawderman, and D. Tang

Hierarchical modelling 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 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.

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