Asymptotic variance and convergence rates of nearly-periodic Markov chain Monte Carlo algorithms

• 成果类型: Article
• 署名作者: Rosenthal, JS
• 署名单位: University of Toronto
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214503388619193
• 发表日期: 2003
• 页码: 169-177
• 关键词: gibbs sampler; computation; bounds

摘要

This article considers nearly-periodic Markov chains that may have excellent functional estimation properties but poor distributional convergence rate. It shows how simple modifications of the chain (involving using a random number of iterations) can greatly improve the distributional convergence of the chain. Various theoretical results about convergence rates of the modified chains are proven. A number of examples, including a transdimensional Markov chain Monte Carlo example, a card-shuffling example, and several antithetic Metropolis algorithms, are considered.