Unbiased Markov chain Monte Carlo methods with couplings
Unbiased Markov chain Monte Carlo methods with couplings
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DOI：
10.1111/rssb.12336
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发表时间：
2020-05-06
影响因子：
5.8
通讯作者：
Atchade, Yves F.
中科院分区：
文献类型：
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作者：
Jacob, Pierre E.;O'Leary, John;Atchade, Yves F.
马尔可夫链蒙特卡罗（MCMC）方法提供了一致的近似积分的迭代次数达到无穷大。MCMC估计量通常在任何固定次数的迭代后都有偏。我们建议通过使用耦合的马尔可夫链连同一个伸缩和参数的格林和李承晚，以消除这种偏见。由此产生的无偏估计可以独立地并行计算。我们讨论流行的MCMC算法的实际耦合。我们建立的估计提出的理论有效性，并研究其效率相对于底层MCMC算法。最后，我们说明了玩具的例子，在伊辛模型的临界温度，在高维变量选择问题，并在贝叶斯推理模型的多个模块的近似切割分布的方法的性能和局限性。
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.