Atchadé, Yves F.; Roberts, Gareth O.; Rosenthal, Jeffrey S. Towards optimal scaling of Metropolis-coupled Markov chain Monte Carlo. (English) Zbl 1223.65001 Stat. Comput. 21, No. 4, 555-568 (2011). Summary: 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. Cited in 22 Documents MSC: 65C05 Monte Carlo methods 65C40 Numerical analysis or methods applied to Markov chains 60J22 Computational methods in Markov chains 60G50 Sums of independent random variables; random walks Keywords:simulated tempering; optimal scaling; Metropolis-Hastings algorithm; Markov chain; Monte Carlo algorithm; random walk PDFBibTeX XMLCite \textit{Y. F. Atchadé} et al., Stat. Comput. 21, No. 4, 555--568 (2011; Zbl 1223.65001) Full Text: DOI References: [1] Andrieu, C., Moulines, E.: On the ergodicity properties of some Markov chain Monte Carlo algorithms. Ann. Appl. Probab. 44(2), 458–475 (2007) [2] Andrieu, C., Robert, C.P.: Controlled MCMC for optimal sampling. Preprint (2001) [3] Atchade, Y.F.: An adaptive version of the Metropolis adjusted Langevin algorithm with a truncated drift. Methodol. Comput. Appl. 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