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ANALYSIS AND OPTIMIZATION OF CERTAIN PARALLEL MONTE CARLO METHODS IN THE LOW TEMPERATURE LIMIT
Brown Univ, Div Appl Math, Providence, RI 02912 USA..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0003-0053-0485
2022 (English)In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 20, no 1, p. 220-249Article in journal (Refereed) Published
Abstract [en]

Metastability is a formidable challenge to Markov chain Monte Carlo methods. In this paper we present methods for algorithm design to meet this challenge. The design problem we consider is temperature selection for the infinite swapping scheme, which is the limit of the widely used parallel tempering scheme obtained when the swap rate tends to infinity. We use a recently developed tool for the analysis of the empirical measure of a small noise diffusion to transform the variance reduction problem into an explicit optimization problem. Our first analysis of the optimization problem is in the setting of a double-well model, and it shows that the optimal selection of temperature ratios is a geometric sequence except possibly the highest temperature. In the same setting we identify two different sources of variance reduction and show how their competition determines the optimal highest temperature. In the general multiwell setting we prove that the same geometric sequence of temperature ratios as in the two-well case is always nearly optimal, with a performance gap that decays geometrically in the number of temperatures.

Place, publisher, year, edition, pages
SIAM PUBLICATIONS , 2022. Vol. 20, no 1, p. 220-249
Keywords [en]
parallel tempering, infinite swapping, Monte Carlo, large deviations, Gibbs mea-sures, variance reduction
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-315896DOI: 10.1137/21M1402029ISI: 000824439400003Scopus ID: 2-s2.0-85130517825OAI: oai:DiVA.org:kth-315896DiVA, id: diva2:1684815
Note

QC 20220728

Available from: 2022-07-28 Created: 2022-07-28 Last updated: 2022-07-28Bibliographically approved

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Wu, Guo-Jhen

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CiteExportLink to record
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