Couplings play a central role in contemporary Markov chain Monte Carlo methods and in the analysis of their convergence to stationarity. In most cases, a coupling must induce relatively fast meeting between chains to ensure good performance. In this paper we fix attention on the random walk Metropolis algorithm and examine a range of coupling design choices. We introduce proposal and acceptance step couplings based on geometric, optimal transport, and maximality considerations. We consider the theoretical properties of these choices and examine their implication for the meeting time of the chains. We conclude by extracting a few general principles and hypotheses on the design of effective couplings.

翻译：在现代Markov连锁公司Monte Carlo的方法以及分析它们与固定性之间的趋同方面,组合在当代Markov Monte Carlo方法以及分析这些方法中起着中心作用。在大多数情况下,组合必须促使链子之间相对快的会合,以确保良好的业绩。在本文中,我们关注随机步行大都会算法并研究一系列组合设计选择。我们引入了基于几何、最佳交通和最大度考虑的建议和接受的渐进式组合。我们考虑了这些选择的理论特性,并研究了这些选择对链子会议时间的影响。我们通过提取一些关于有效组合设计的一般原则和假设来得出结论。