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A large deviation analysis of certain qualitative properties of parallel tempering and infinite swapping algorithms
2018 (English)In: Applied mathematics and optimization, ISSN 0095-4616, E-ISSN 1432-0606, Vol. 78, no 1, p. 103-144Article in journal (Refereed) Published
Abstract [en]

Parallel tempering, or replica exchange, is a popular method for simulating complex systems. The idea is to run parallel simulations at different temperatures, and at a given swap rate exchange configurations between the parallel simulations. From the perspective of large deviations it is optimal to let the swap rate tend to infinity and it is possible to construct a corresponding simulation scheme, known as infinite swapping. In this paper we propose a novel use of large deviations for empirical measures for a more detailed analysis of the infinite swapping limit in the setting of continuous time jump Markov processes. Using the large deviations rate function and associated stochastic control problems we consider a diagnostic based on temperature assignments, which can be easily computed during a simulation. We show that the convergence of this diagnostic to its a priori known limit is a necessary condition for the convergence of infinite swapping. The rate function is also used to investigate the impact of asymmetries in the underlying potential landscape, and where in the state space poor sampling is most likely to occur.

Place, publisher, year, edition, pages
Springer, 2018. Vol. 78, no 1, p. 103-144
Keywords [en]
Large deviatins, MCMC, parallel tempering, infinite swapping, ergodic control
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-198612DOI: 10.1007/s00245-017-9401-9ISI: 000438412600004Scopus ID: 2-s2.0-85011844953OAI: oai:DiVA.org:kth-198612DiVA, id: diva2:1057603
Note

QC 20181128

Available from: 2016-12-19 Created: 2016-12-19 Last updated: 2018-11-28Bibliographically approved

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Publisher's full textScopushttps://link.springer.com/article/10.1007/s00245-017-9401-9

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Nyquist, Pierre
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  • nn-NB
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