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Optimal scaling of the random walk Metropolis: general criteria for the 0.234 acceptance rule

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Optimal scaling of the random walk Metropolis: general criteria for the 0.234 acceptance rule. / Sherlock, Christopher.
In: Journal of Applied Probability, Vol. 50, No. 1, 03.2013, p. 1-15.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Sherlock, C 2013, 'Optimal scaling of the random walk Metropolis: general criteria for the 0.234 acceptance rule', Journal of Applied Probability, vol. 50, no. 1, pp. 1-15. https://doi.org/10.1239/jap/1363784420

APA

Sherlock, C. (2013). Optimal scaling of the random walk Metropolis: general criteria for the 0.234 acceptance rule. Journal of Applied Probability, 50(1), 1-15. https://doi.org/10.1239/jap/1363784420

Vancouver

Sherlock C. Optimal scaling of the random walk Metropolis: general criteria for the 0.234 acceptance rule. Journal of Applied Probability. 2013 Mar;50(1):1-15. doi: 10.1239/jap/1363784420

Author

Sherlock, Christopher. / Optimal scaling of the random walk Metropolis : general criteria for the 0.234 acceptance rule. In: Journal of Applied Probability. 2013 ; Vol. 50, No. 1. pp. 1-15.

Bibtex

@article{a145a2872b4f462e8a72f5b96e015602,
title = "Optimal scaling of the random walk Metropolis: general criteria for the 0.234 acceptance rule",
abstract = "Scaling of proposals for Metropolis algorithms is an important practical problem in MCMC implementation. Analyses of the random walk Metropolis for high dimensional targets with specific functional forms have shown that in many cases the optimal scaling is achieved when the acceptance rate is approximately 0.234, but that there are exceptions. We present a general set of sufficient conditions which are invariant to orthonormal transformation of the co-ordinate axes and which ensure that the limiting optimal acceptance rate is 0.234. The criteria are shown to hold for the joint distribution of successive elements of a stationary p-th order multivariate Markov process.",
keywords = "Random walk Metropolis, optimal scaling, optimal acceptance rate",
author = "Christopher Sherlock",
year = "2013",
month = mar,
doi = "10.1239/jap/1363784420",
language = "English",
volume = "50",
pages = "1--15",
journal = "Journal of Applied Probability",
publisher = "University of Sheffield",
number = "1",

}

RIS

TY - JOUR

T1 - Optimal scaling of the random walk Metropolis

T2 - general criteria for the 0.234 acceptance rule

AU - Sherlock, Christopher

PY - 2013/3

Y1 - 2013/3

N2 - Scaling of proposals for Metropolis algorithms is an important practical problem in MCMC implementation. Analyses of the random walk Metropolis for high dimensional targets with specific functional forms have shown that in many cases the optimal scaling is achieved when the acceptance rate is approximately 0.234, but that there are exceptions. We present a general set of sufficient conditions which are invariant to orthonormal transformation of the co-ordinate axes and which ensure that the limiting optimal acceptance rate is 0.234. The criteria are shown to hold for the joint distribution of successive elements of a stationary p-th order multivariate Markov process.

AB - Scaling of proposals for Metropolis algorithms is an important practical problem in MCMC implementation. Analyses of the random walk Metropolis for high dimensional targets with specific functional forms have shown that in many cases the optimal scaling is achieved when the acceptance rate is approximately 0.234, but that there are exceptions. We present a general set of sufficient conditions which are invariant to orthonormal transformation of the co-ordinate axes and which ensure that the limiting optimal acceptance rate is 0.234. The criteria are shown to hold for the joint distribution of successive elements of a stationary p-th order multivariate Markov process.

KW - Random walk Metropolis

KW - optimal scaling

KW - optimal acceptance rate

U2 - 10.1239/jap/1363784420

DO - 10.1239/jap/1363784420

M3 - Journal article

VL - 50

SP - 1

EP - 15

JO - Journal of Applied Probability

JF - Journal of Applied Probability

IS - 1

ER -