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Extended Ensemble Monte Carlo

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  • YUKITO IBA

    (The Institute of Statistical Mathematics, Japan)

Abstract

"Extended Ensemble Monte Carlo" is a generic term that indicates a set of algorithms, which are now popular in a variety of fields in physics and statistical information processing. Exchange Monte Carlo (Metropolis-Coupled Chain, Parallel Tempering), Simulated Tempering (Expanded Ensemble Monte Carlo) and Multicanonical Monte Carlo (Adaptive Umbrella Sampling) are typical members of this family. Here, we give a cross-disciplinary survey of these algorithms with special emphasis on the great flexibility of the underlying idea. In Sec. 2, we discuss the background of Extended Ensemble Monte Carlo. In Secs. 3, 4 and 5, three types of the algorithms, i.e., Exchange Monte Carlo, Simulated Tempering, Multicanonical Monte Carlo, are introduced. In Sec. 6, we give an introduction to Replica Monte Carlo algorithm by Swendsen and Wang. Strategies for the construction of special-purpose extended ensembles are discussed in Sec. 7. We stress that an extension is not necessary restricted to the space of energy or temperature. Even unphysical (unrealizable) configurations can be included in the ensemble, if the resultant fast mixing of the Markov chain offsets the increasing cost of the sampling procedure. Multivariate (multicomponent) extensions are also useful in many examples. In Sec. 8, we give a survey on extended ensembles with a state space whose dimensionality is dynamically varying. In the appendix, we discuss advantages and disadvantages of three types of extended ensemble algorithms.

Suggested Citation

  • Yukito Iba, 2001. "Extended Ensemble Monte Carlo," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(05), pages 623-656.
    • Handle: RePEc:wsi:ijmpcx:v:12:y:2001:i:05:n:s0129183101001912
    DOI: 10.1142/S0129183101001912
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    Citations

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    Cited by:

    1. Enrico Petretto & Leonardo Bottolo & Sarah R Langley & Matthias Heinig & Chris McDermott-Roe & Rizwan Sarwar & Michal Pravenec & Norbert Hübner & Timothy J Aitman & Stuart A Cook & Sylvia Richardson, 2010. "New Insights into the Genetic Control of Gene Expression using a Bayesian Multi-tissue Approach," PLOS Computational Biology, Public Library of Science, vol. 6(4), pages 1-13, April.
    2. Nicolas Chopin & Tony Lelievre & Gabriel Stoltz, 2010. "Free Energy Methods for Efficient Exploration of Mixture Posterior Densities," Working Papers 2010-33, Center for Research in Economics and Statistics.
    3. Kato, Kensuke, 2016. "Long-range Ising model for credit portfolios with heterogeneous credit exposures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1103-1119.
    4. Yukito Iba & Nen Saito & Akimasa Kitajima, 2014. "Multicanonical MCMC for sampling rare events: an illustrative review," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 611-645, June.
    5. Rigat, F. & Mira, A., 2012. "Parallel hierarchical sampling: A general-purpose interacting Markov chains Monte Carlo algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1450-1467.

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