论文标题
一种减少MCMC差异的分裂方法
A splitting method to reduce MCMC variance
论文作者
论文摘要
我们探讨了分裂和杀戮方法是否可以提高马尔可夫链蒙特卡洛（MCMC）对罕见事件概率的估计的准确性，并且我们做出了三个贡献。首先，我们证明“加权集合”是唯一与MCMC结合使用渐近一致估计的分裂和杀戮方法。其次，我们证明了加权集合估计值的渐近方差的下限。第三，我们给出一个建设性的证明和数值示例，以表明加权集合可以接近这种最佳方差结合，在许多情况下，MCMC估计值的方差减少了多个数量级。
We explore whether splitting and killing methods can improve the accuracy of Markov chain Monte Carlo (MCMC) estimates of rare event probabilities, and we make three contributions. First, we prove that "weighted ensemble" is the only splitting and killing method that provides asymptotically consistent estimates when combined with MCMC. Second, we prove a lower bound on the asymptotic variance of weighted ensemble's estimates. Third, we give a constructive proof and numerical examples to show that weighted ensemble can approach this optimal variance bound, in many cases reducing the variance of MCMC estimates by multiple orders of magnitude.
