Posterior propriety and admissibility of hyperpriors in normal hierarchical models

TY - JOUR

T1 - Posterior propriety and admissibility of hyperpriors in normal hierarchical models

AU - Berger, James O.

AU - Strawderman, William

AU - Tang, Dejun

PY - 2005/4

Y1 - 2005/4

N2 - 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.

AB - 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.

KW - Covariance matrix

KW - Frequentist risk

KW - Markov chain Monte Carlo

KW - Objective priors

KW - Posterior impropriety

KW - Quadratic loss

UR - http://www.scopus.com/inward/record.url?scp=22944461401&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22944461401&partnerID=8YFLogxK

U2 - https://doi.org/10.1214/009053605000000075

DO - https://doi.org/10.1214/009053605000000075

M3 - Article

VL - 33

SP - 606

EP - 646

JO - Annals of Statistics

JF - Annals of Statistics

SN - 0090-5364

IS - 2

ER -