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September 2006 Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper)
Andrew Gelman
Bayesian Anal. 1(3): 515-534 (September 2006). DOI: 10.1214/06-BA117A


Various noninformative prior distributions have been suggested for scale parameters in hierarchical models. We construct a new folded-noncentral-$t$ family of conditionally conjugate priors for hierarchical standard deviation parameters, and then consider noninformative and weakly informative priors in this family. We use an example to illustrate serious problems with the inverse-gamma family of "noninformative" prior distributions. We suggest instead to use a uniform prior on the hierarchical standard deviation, using the half-$t$ family when the number of groups is small and in other settings where a weakly informative prior is desired. We also illustrate the use of the half-$t$ family for hierarchical modeling of multiple variance parameters such as arise in the analysis of variance.


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Andrew Gelman. "Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper)." Bayesian Anal. 1 (3) 515 - 534, September 2006.


Published: September 2006
First available in Project Euclid: 22 June 2012

zbMATH: 1331.62139
MathSciNet: MR2221284
Digital Object Identifier: 10.1214/06-BA117A

Keywords: Bayesian inference , conditional conjugacy , folded-noncentral-$t$ distribution , half-$t$ distribution , hierarchical model , multilevel model , noninformative prior distribution , weakly informative prior distribution

Rights: Copyright © 2006 International Society for Bayesian Analysis


Vol.1 • No. 3 • September 2006
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