Rates of convergence of the Hastings and Metropolis algorithms

• 成果类型: Article
• 署名作者: Mengersen, KL; Tweedie, RL
• 署名单位: Colorado State University System; Colorado State University Fort Collins
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 101-121
• 关键词: bayesian computation; GIBBS SAMPLER; statistics

摘要

We apply recent results in Markov chain theory to Hastings and Metropolis algorithms with either independent or symmetric candidate distributions, and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution pi. In the independence case (in R(k)) these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of pi; in the symmetric case (in R only) we show geometric convergence essentially occurs if and only if pi has geometric tails. We also evaluate recently developed computable bounds on the rates of convergence in this context: examples show that these theoretical bounds can be inherently extremely conservative, although when the chain is stochastically monotone the bounds may well be effective.