We introduce a generalised micro-macro Markov chain Monte Carlo (mM-MCMC) method with pseudo-marginal approximation to the free energy, that is able to accelerate sampling of the microscopic Gibbs distributions when there is a time-scale separation between the macroscopic dynamics of a reaction coordinate and the remaining microscopic degrees of freedom. The mM-MCMC method attains this efficiency by iterating four steps: i) Propose a new value of the reaction coordinate; ii) Accept or reject the macroscopic sample; iii) Run a biased simulation that creates a microscopic molecular instance that lies close to the newly sampled macroscopic reaction coordinate value; iv) Microscopic accept/reject step for the new microscopic sample. In the present paper, we eliminate the main computational bottleneck of earlier versions of this method: the necessity to have an accurate approximation of the free energy. We show that introduction of a pseudo-marginal approximation significantly reduces the computational cost of the microscopic accept/reject step, while still providing unbiased samples. We illustrate the method's behaviour on several molecular systems with low-dimensional reaction coordinates.

翻译：摘要：我们提出了一种具有自由能伪边缘近似的广义微宏观马尔可夫链蒙特卡洛（mM-MCMC）方法，当反应坐标的宏观动力学与其余微观自由度之间存在时间尺度分离时，该方法能够加速微观吉布斯分布的采样。mM-MCMC方法通过迭代四个步骤实现这一效率：i) 提出反应坐标的新值；ii) 接受或拒绝宏观样本；iii) 运行有偏模拟，生成接近新采样宏观反应坐标值的微观分子实例；iv) 对新微观样本执行微观接受/拒绝步骤。在本文中，我们消除了该方法早期版本的主要计算瓶颈：即需要精确近似自由能。我们证明，引入伪边缘近似可显著降低微观接受/拒绝步骤的计算成本，同时仍能提供无偏样本。我们通过几个具有低维反应坐标的分子系统展示了该方法的行为。