The Annals of Statistics

Stability of the Gibbs sampler for Bayesian hierarchical models

Omiros Papaspiliopoulos and Gareth Roberts

Full-text: Open access

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.

Article information

Source
Ann. Statist. Volume 36, Number 1 (2008), 95-117.

Dates
First available in Project Euclid: 1 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1201877295

Digital Object Identifier
doi:10.1214/009053607000000749

Mathematical Reviews number (MathSciNet)
MR2387965

Zentralblatt MATH identifier
1144.65007

Subjects
Primary: 65C05: Monte Carlo methods
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces

Keywords
Geometric ergodicity capacitance collapsed Gibbs sampler state-space models parametrization Bayesian robustness

Citation

Papaspiliopoulos, Omiros; Roberts, Gareth. Stability of the Gibbs sampler for Bayesian hierarchical models. Ann. Statist. 36 (2008), no. 1, 95--117. doi:10.1214/009053607000000749. https://projecteuclid.org/euclid.aos/1201877295


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