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An ergodic theorem for the weighted ensemble method

Part of: Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  18 January 2022

David Aristoff
David Aristoff*
Affiliation:
Colorado State University
*
*Postal address: 841 Oval Drive, Fort Collins, CO 80523, USA. Email address: aristoff@math.colostate.edu
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Abstract

We study weighted ensemble, an interacting particle method for sampling distributions of Markov chains that has been used in computational chemistry since the 1990s. Many important applications of weighted ensemble require the computation of long time averages. We establish the consistency of weighted ensemble in this setting by proving an ergodic theorem for time averages. As part of the proof, we derive explicit variance formulas that could be useful for optimizing the method.

Keywords

Interacting particle systemsequential Monte Carloergodic theoremweighted ensembleimportance samplingsteady statestratification

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 65C35: Stochastic particle methods 65C40: Computational Markov chains
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 1 , March 2022 , pp. 152 - 166
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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