Monte Carlo methods - such as Markov chain Monte Carlo (MCMC) and piecewise deterministic Markov process (PDMP) samplers - provide asymptotically exact estimators of expectations under a target distribution. There is growing interest in alternatives to this asymptotic regime, in particular in constructing estimators that are exact in the limit of an infinite amount of computing processors, rather than in the limit of an infinite number of Markov iterations. In particular, Jacob et al. (2020) introduced coupled MCMC estimators to remove the non-asymptotic bias, resulting in MCMC estimators that can be embarrassingly parallelised. In this work, we extend the estimators of Jacob et al. (2020) to the continuous-time context and derive couplings for the bouncy, the boomerang and the coordinate samplers. Some preliminary empirical results are included that demonstrate the reasonable scaling of our method with the dimension of the target.

翻译：蒙特卡洛方法——如马尔可夫链蒙特卡洛（MCMC）和分段确定性马尔可夫过程（PDMP）采样器——能够提供目标分布下期望的渐近精确估计。目前，人们越来越关注这种渐近机制的替代方案，特别是构造在无限计算处理器极限下精确而非无限马尔可夫迭代极限下的估计器。具体而言，Jacob等人（2020）引入了耦合MCMC估计器以消除非渐近偏差，从而得到可轻松并行化的MCMC估计器。在本工作中，我们将Jacob等人（2020）的估计器扩展到连续时间场景，并为反弹采样器、回旋镖采样器和坐标采样器推导了耦合方法。文中还包含初步实证结果，展示了我们的方法在目标维度上的合理扩展性。