论文标题
大都会杂货算法的最大耦合
Maximal couplings of the Metropolis-Hastings algorithm
论文作者
论文摘要
耦合在分析Markov链蒙特卡洛算法中起着核心作用，并且越来越多地出现在算法本身中，例如在收敛诊断，并行化和降低方差技术中。大都会杂货店算法的现有耦合分别处理提案和接受步骤，并且在耦合不平等给出的一步会议概率上的上限不足。本文介绍了最大耦合，这些耦合在保留当前方法的实际优势的同时，达到了这种界限。我们考虑这些耦合的特性，并在选择数值示例中检查它们的行为。
Couplings play a central role in the analysis of Markov chain Monte Carlo algorithms and appear increasingly often in the algorithms themselves, e.g. in convergence diagnostics, parallelization, and variance reduction techniques. Existing couplings of the Metropolis-Hastings algorithm handle the proposal and acceptance steps separately and fall short of the upper bound on one-step meeting probabilities given by the coupling inequality. This paper introduces maximal couplings which achieve this bound while retaining the practical advantages of current methods. We consider the properties of these couplings and examine their behavior on a selection of numerical examples.
