Variance bounding Markov chains

• 成果类型: Article
• 署名作者: Roberts, Gareth O.; Rosenthal, Jeffrey S.
• 署名单位: Lancaster University; University of Toronto
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP486
• 发表日期: 2008
• 页码: 1201-1214
• 关键词: exploring posterior distributions; monte-carlo; metropolis algorithms; convergence-rates; GIBBS SAMPLER; hastings

摘要

We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity. Furthermore, variance bounding is equivalent to the existence of usual central limit theorems for all L-2 functionals. Also, variance bounding (unlike geometric ergodicity) is preserved under the Peskun order. We close with some applications to Metropolis-Hastings algorithms.