Autocorrelations in MCMC chains increase the variance of the estimators they produce. We propose the occlusion process to mitigate this problem. It is a process that sits upon an existing MCMC sampler, and occasionally replaces its samples with ones that are decorrelated from the chain. We show that this process inherits many desirable properties from the underlying MCMC sampler, such as a Law of Large Numbers, convergence in a normed function space, and geometric ergodicity, to name a few. We show how to simulate the occlusion process at no additional time-complexity to the underlying MCMC chain. This requires a threaded computer, and a variational approximation to the target distribution. We demonstrate empirically the occlusion process' decorrelation and variance reduction capabilities on two target distributions. The first is a bimodal Gaussian mixture model in 1d and 100d. The second is the Ising model on an arbitrary graph, for which we propose a novel variational distribution.

翻译：MCMC链中的自相关性会增大其估计量的方差。本文提出遮挡过程以缓解该问题。该过程构建于现有MCMC采样器之上，通过间歇性地用与链解相关的样本替换原采样值。我们证明该过程继承了底层MCMC采样器的诸多优良特性，包括大数定律、赋范函数空间中的收敛性以及几何遍历性等。我们展示了如何在不增加底层MCMC链时间复杂度的前提下模拟遮挡过程，这需要具备多线程计算能力及目标分布的变分近似。通过两个目标分布的实验，我们实证验证了遮挡过程的解相关与方差缩减能力：其一是1维与100维的双峰高斯混合模型；其二是任意图结构上的伊辛模型——针对后者我们提出了一种新颖的变分分布。