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Posterior propriety and admissibility of hyperpriors in normal hierarchical models

Publication ,  Journal Article
Berger, JO; Strawderman, W; Tang, D
Published in: Annals of Statistics
April 1, 2005

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. © Institute of Mathematical Statistics, 2005.

Duke Scholars

Published In

Annals of Statistics

DOI

ISSN

0090-5364

Publication Date

April 1, 2005

Volume

33

Issue

2

Start / End Page

606 / 646

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0102 Applied Mathematics
 

Citation

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ICMJE
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Berger, J. O., Strawderman, W., & Tang, D. (2005). Posterior propriety and admissibility of hyperpriors in normal hierarchical models. Annals of Statistics, 33(2), 606–646. https://doi.org/10.1214/009053605000000075
Berger, J. O., W. Strawderman, and D. Tang. “Posterior propriety and admissibility of hyperpriors in normal hierarchical models.” Annals of Statistics 33, no. 2 (April 1, 2005): 606–46. https://doi.org/10.1214/009053605000000075.
Berger JO, Strawderman W, Tang D. Posterior propriety and admissibility of hyperpriors in normal hierarchical models. Annals of Statistics. 2005 Apr 1;33(2):606–46.
Berger, J. O., et al. “Posterior propriety and admissibility of hyperpriors in normal hierarchical models.” Annals of Statistics, vol. 33, no. 2, Apr. 2005, pp. 606–46. Scopus, doi:10.1214/009053605000000075.
Berger JO, Strawderman W, Tang D. Posterior propriety and admissibility of hyperpriors in normal hierarchical models. Annals of Statistics. 2005 Apr 1;33(2):606–646.

Published In

Annals of Statistics

DOI

ISSN

0090-5364

Publication Date

April 1, 2005

Volume

33

Issue

2

Start / End Page

606 / 646

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0102 Applied Mathematics