Stratification as a General Variance Reduction Method for Markov Chain Monte Carlo

Aaron R. Dinner, Erik H. Thiede, Brian van Koten, Jonathan Weare

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1139-1188
Number of pages50
JournalSIAM-ASA Journal on Uncertainty Quantification
Volume8
Issue number3
DOIs
StatePublished - Aug 24 2020

Keywords

  • Markov chain Monte Carlo
  • Stratified sampling
  • Variance reduction

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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