Stratification as a general variance reduction method for Markov chain Monte Carlo.
Stratification as a general variance reduction method for Markov chain Monte Carlo.
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DOI：
10.1137/18m122964x
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Weare J
中科院分区：
文献类型：
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作者：
Dinner AR;Thiede EH;Van Koten B;Weare J
伞式抽样特征向量法（Eigenvector Method for Umbrella Sampling，EMUS）是统计力学中一类比较流行的方法，它将分层抽样的原理应用于自由能的计算。本文对EMUS进行了详细的理论分析。基于这种分析，我们表明，EMUS是一个有效的一般方法计算平均任意目标分布。特别是，我们表明，EMUS可以显着更有效地比直接MCMC时，目标分布是多模态或当目标是计算尾部概率。为了说明这些理论结果，我们提出了一个教程应用的方法从贝叶斯统计的问题。
The Eigenvector Method for Umbrella Sampling (EMUS) 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.