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.

马尔可夫链蒙特卡罗 (MCMC) 是一种强大的后验分布逼近方法。然而，MCMC 的迭代特性并不能自然地促进其在 HPC 和云环境上与现代高度并行计算的使用。另一个问题是识别产生的平均值的偏差和蒙特卡罗误差。上述情况促使最近开发了基于 MCMC 算法耦合的完全（“令人尴尬”）并行无偏蒙特卡罗方法。需要注意的是，有效耦合的制定通常不是微不足道的，并且需要特定于模型的技术努力。我们通过考虑自适应 SMC 方法并结合状态空间模型无偏估计的最新进展，提出了源自顺序蒙特卡洛 (SMC) 的 MCMC 链的耦合。然后在 SMC 级别实现耦合，并且原则上不是针对特定问题的。由此产生的方法具有理想的理论特性。与相关文献中通常考虑的目标相比，核心动机是将无偏见的 MCMC 扩展到更具挑战性的目标。我们通过应用到两个复杂的统计模型来说明算法的有效性：（i）马蹄回归；(ii) 高斯图模型。