Stratification as a general variance reduction method for Markov chain Monte Carlo
Methodology
2020-06-22 v3 Numerical Analysis
Numerical Analysis
Computational Physics
Abstract
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.
Keywords
Cite
@article{arxiv.1705.08445,
title = {Stratification as a general variance reduction method for Markov chain Monte Carlo},
author = {Aaron R. Dinner and Erik Thiede and Brian Van Koten and Jonathan Weare},
journal= {arXiv preprint arXiv:1705.08445},
year = {2020}
}
Comments
52 pages, 11 figures