@article{1dc10faf96194e9192d95be05e3e75be,
title = "Stratification as a General Variance Reduction Method for Markov Chain Monte Carlo",
abstract = "The Eigenvector Method for Umbrella Sampling (EMUS) [46] 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. ",
keywords = "Markov chain Monte Carlo, Stratified sampling, Variance reduction",
author = "Dinner, {Aaron R.} and Thiede, {Erik H.} and {van Koten}, Brian and Jonathan Weare",
note = "Funding Information: \ast Received by the editors December 3, 2018; accepted for publication (in revised form) April 27, 2020; published electronically August 24, 2020. https://doi.org/10.1137/18M122964X Funding: The work of the first and second authors was supported by National Institutes of Health (NIH) grant 5 R01 GM109455. The work of the third author was supported by NSF RTG: Computational and Applied Mathematics in Statistical Science, 1547396. The fourth author was also supported by the Advanced Scientific Computing Research Program within the DOE Office of Science through award DE-SC0020427. Computing resources were provided by the University of Chicago Research Computing Center. \dagger Department of Chemistry and James Franck Institute, the University of Chicago, Chicago, IL 60637 (
[email protected],
[email protected]). \ddagger Department of Mathematics and Statistics, the University of Massachusetts, Amherst, MA 01003 (
[email protected]). \S Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 (
[email protected]). Funding Information: The work of the first and second authors was supported by National Institutes of Health (NIH) grant 5 R01 GM109455. The work of the third author was supported by NSF RTG: Computational and Applied Mathematics in Statistical Science, 1547396. The fourth author was also supported by the Advanced Scientific Computing Research Program within the DOE Office of Science through award DE-SC0020427. Computing resources were provided by the University of Chicago Research Computing Center. We wish to thank Jonathan Mattingly, Jeremy Tempkin, and Charlie Matthews for helpful discussions. Publisher Copyright: {\textcopyright} 2020 Society for Industrial and Applied Mathematics and American Statistical Association",
year = "2020",
month = aug,
day = "24",
doi = "10.1137/18M122964X",
language = "English (US)",
volume = "8",
pages = "1139--1188",
journal = "SIAM-ASA Journal on Uncertainty Quantification",
issn = "2166-2525",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",
}