Towards optimal scaling of metropolis-coupled Markov chain Monte Carlo

Authors:
Yves F. Atchadé;Gareth O. Roberts;Jeffrey S. Rosenthal
Affiliations:
Department of Statistics, University of Michigan, Ann Arbor, USA 48109;Department of Statistics, University of Warwick, Coventry, UK CV4 7AL;Department of Statistics, University of Toronto, Toronto, Canada M5S 3G3
Venue:
Statistics and Computing
Year:
2011

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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.