SIAM/ASA Journal on Uncertainty Quantification, Volume 8, Issue 3, Page 1139-1188, January 2020.
The eigenvector method for umbrella sampling (EMUS) [E. H. Thiede et al., J. Chem. Phys., 145 (2016), 084115] belongs to a popular class of methods in statistical mechanics which adapt the principle of stratified survey sampling to the computation of free energies. We develop a detailed theoretical analysis of EMUS. Based on this analysis, we show that EMUS is an efficient general method for computing averages over arbitrary target distributions. In particular, we show that EMUS can be dramatically more efficient than direct MCMC when the target distribution is multimodal or when the goal is to compute tail probabilities. To illustrate these theoretical results, we present a tutorial application of the method to a problem from Bayesian statistics.

中文翻译：

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分层作为马尔可夫链蒙特卡罗的一般方差减少方法

SIAM/ASA 不确定性量化杂志，第 8 卷，第 3 期，第 1139-1188 页，2020 年 1 月。
伞形采样 (EMUS) 的特征向量方法 [EH Thiede 等人，J. Chem. Phys., 145 (2016), 084115] 属于统计力学中的一类流行方法，它采用分层调查抽样的原则来计算自由能。我们对 EMUS 进行了详细的理论分析。基于此分析，我们表明 EMUS 是一种有效的通用方法，可用于计算任意目标分布的平均值。特别是，当目标分布是多模态或目标是计算尾部概率时，我们表明 EMUS 比直接 MCMC 更有效。为了说明这些理论结果，我们提出了将该方法应用于贝叶斯统计问题的教程。