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Towards optimal scaling of metropolis-coupled Markov chain Monte Carlo

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Abstract

We consider optimal temperature spacings for Metropolis-coupled Markov chain Monte Carlo (MCMCMC) and Simulated Tempering algorithms. We prove that, under certain conditions, it is optimal (in terms of maximising the expected squared jumping distance) to space the temperatures so that the proportion of temperature swaps which are accepted is approximately 0.234. This generalises related work by physicists, and is consistent with previous work about optimal scaling of random-walk Metropolis algorithms.

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Authors and Affiliations

  1. Department of Statistics, University of Michigan, 1085 South University, Ann Arbor, 48109, MI, USA

    Yves F. Atchadé

  2. Department of Statistics, University of Warwick, Coventry, CV4 7AL, UK

    Gareth O. Roberts

  3. Department of Statistics, University of Toronto, Toronto, Ontario, Canada, M5S 3G3

    Jeffrey S. Rosenthal

Authors
  1. Yves F. Atchadé
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  2. Gareth O. Roberts
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  3. Jeffrey S. Rosenthal
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Corresponding author

Correspondence to Jeffrey S. Rosenthal.

Additional information

J.S. Rosenthal is partially supported by NSERC of Canada.

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Atchadé, Y.F., Roberts, G.O. & Rosenthal, J.S. Towards optimal scaling of metropolis-coupled Markov chain Monte Carlo. Stat Comput 21, 555–568 (2011). https://doi.org/10.1007/s11222-010-9192-1

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  • DOI: https://doi.org/10.1007/s11222-010-9192-1

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