Unbiased Markov chain Monte Carlo methods with couplings

• 成果类型: Article
• 署名作者: Jacob, Pierre E.; O'Leary, John; Atchade, Yves F.
• 署名单位: Harvard University; Boston University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12336
• 发表日期: 2020
• 页码: 543-600
• 关键词: geometric ergodicity; convergence-rates; bayesian-analysis; GIBBS SAMPLER; simulation; hastings; algorithm; regeneration; MODEL; state

摘要

Markov chain Monte Carlo (MCMC) methods provide consistent approximations of integrals as the number of iterations goes to infinity. MCMC estimators are generally biased after any fixed number of iterations. We propose to remove this bias by using couplings of Markov chains together with a telescopic sum argument of Glynn and Rhee. The resulting unbiased estimators can be computed independently in parallel. We discuss practical couplings for popular MCMC algorithms. We establish the theoretical validity of the estimators proposed and study their efficiency relative to the underlying MCMC algorithms. Finally, we illustrate the performance and limitations of the method on toy examples, on an Ising model around its critical temperature, on a high dimensional variable-selection problem, and on an approximation of the cut distribution arising in Bayesian inference for models made of multiple modules.