On convergence rates of Gibbs samplers for uniform distributions

• 成果类型: Article
• 署名作者: Roberts, GO; Rosenthal, JS
• 署名单位: University of Cambridge; University of Toronto
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 1998
• 页码: 1291-1302
• 关键词: markov-chains

摘要

We consider a Gibbs sampler applied to the uniform distribution on a bounded region R subset of or equal to R-d. We show that the convergence properties of the Gibbs sampler depend greatly on the smoothness of the boundary of R. Indeed, for sufficiently smooth boundaries the sampler is uniformly ergodic, while for jagged boundaries the sampler could fail to even be geometrically ergodic.