Abstract
Various noninformative prior distributions have been suggested for scale parameters in\nhierarchical models. We construct a new folded-noncentral-$t$ family of conditionally\nconjugate priors for hierarchical standard deviation parameters, and then consider\nnoninformative and weakly informative priors in this family. We use an example to\nillustrate serious problems with the inverse-gamma family of "noninformative" prior\ndistributions. We suggest instead to use a uniform prior on the hierarchical standard\ndeviation, using the half-$t$ family when the number of groups is small and in other\nsettings where a weakly informative prior is desired. We also illustrate the use of the\nhalf-$t$ family for hierarchical modeling of multiple variance parameters such as arise\nin the analysis of variance.
Keywords
Prior probabilityVariance (accounting)MathematicsHierarchical database modelStatisticsStandard deviationConjugate priorEconometricsComputer scienceBayesian probabilityData mining
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Publication Info
- Year
- 2006
- Type
- article
- Volume
- 1
- Issue
- 3
- Citations
- 3940
- Access
- Closed
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Cite This
Andrew Gelman
(2006).
Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper).
Bayesian Analysis
, 1
(3)
.
https://doi.org/10.1214/06-ba117a
Identifiers
- DOI
- 10.1214/06-ba117a