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Stability of the Gibbs sampler for Bayesian hierarchical models
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Papaspiliopoulos, Omiros and Roberts, Gareth O. (2008) Stability of the Gibbs sampler for Bayesian hierarchical models. Annals of statistics, Vol.36 (No.1). pp. 95-117. doi:10.1214/009053607000000749 ISSN 0090-5364.
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Official URL: http://dx.doi.org/10.1214/009053607000000749
Abstract
We characterize the convergence of the Gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions. We show that the convergence can be uniform, geometric or subgeometric depending on the relative tail behavior of the error distributions, and on the parametrization chosen. Our theory is applied to characterize the convergence of the Gibbs sampler on latent Gaussian process models. We indicate how the theoretical framework we introduce will be useful in analyzing more complex models.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Bayesian statistical decision theory, Mathematical constants, Gibbs' equation | ||||
Journal or Publication Title: | Annals of statistics | ||||
Publisher: | Inst Mathematical Statistics | ||||
ISSN: | 0090-5364 | ||||
Official Date: | February 2008 | ||||
Dates: |
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Volume: | Vol.36 | ||||
Number: | No.1 | ||||
Number of Pages: | 23 | ||||
Page Range: | pp. 95-117 | ||||
DOI: | 10.1214/009053607000000749 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published |
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