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February 2008 Stability of the Gibbs sampler for Bayesian hierarchical models
Omiros Papaspiliopoulos, Gareth Roberts
Ann. Statist. 36(1): 95-117 (February 2008). DOI: 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.

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Omiros Papaspiliopoulos. Gareth Roberts. "Stability of the Gibbs sampler for Bayesian hierarchical models." Ann. Statist. 36 (1) 95 - 117, February 2008. https://doi.org/10.1214/009053607000000749

Information

Published: February 2008
First available in Project Euclid: 1 February 2008

zbMATH: 1144.65007
MathSciNet: MR2387965
Digital Object Identifier: 10.1214/009053607000000749

Subjects:
Primary: 65C05
Secondary: 60J27

Keywords: Bayesian robustness , capacitance , collapsed Gibbs sampler , geometric ergodicity , parametrization , state-space models

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 1 • February 2008
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