Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallel computation on HPC and cloud environments. Another concern is the identification of the bias and Monte Carlo error of produced averages. The above have prompted the recent development of fully ('embarrassingly') parallel unbiased Monte Carlo methodology based on coupling of MCMC algorithms. A caveat is that formulation of effective coupling is typically not trivial and requires model-specific technical effort. We propose coupling of MCMC chains deriving from sequential Monte Carlo (SMC) by considering adaptive SMC methods in combination with recent advances in unbiased estimation for state-space models. Coupling is then achieved at the SMC level and is, in principle, not problem-specific. The resulting methodology enjoys desirable theoretical properties. A central motivation is to extend unbiased MCMC to more challenging targets compared to the ones typically considered in the relevant literature. We illustrate the effectiveness of the algorithm via application to two complex statistical models: (i) horseshoe regression; (ii) Gaussian graphical models.

翻译：马尔可夫链蒙特卡洛（MCMC）方法是逼近后验分布的有力工具。然而，MCMC的迭代特性使其难以自然适应高性能计算（HPC）和云环境中高度并行的现代计算需求。此外，如何识别所产生的平均值的偏差和蒙特卡洛误差也是另一关键问题。上述挑战催生了近期基于MCMC算法耦合的完全（“尴尬”）并行无偏蒙特卡洛方法的发展。但需要指出的是，设计有效的耦合通常并非易事，且需要针对具体模型投入专门的技术努力。我们提出通过结合自适应SMC方法与状态空间模型无偏估计的最新进展，实现源自序贯蒙特卡洛（SMC）的MCMC链的耦合。这种耦合在SMC层面完成，原则上不依赖于具体问题。该方法具有理想的理论性质。其核心动机是将无偏MCMC扩展至比相关文献中通常考虑的更具挑战性的目标。我们通过两个复杂统计模型的应用验证了算法的有效性：（i）马蹄形回归；（ii）高斯图模型。