Stability of the Gibbs sampler for Bayesian hierarchical models

• 成果类型: Article
• 署名作者: Papaspiliopoulos, Omiros; Roberts, Gareth
• 署名单位: University of Warwick
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000749
• 发表日期: 2008
• 页码: 95-117
• 关键词: markov-chains

摘要

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.