Journal of Applied Probability

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

Chris Sherlock

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Abstract

Scaling of proposals for Metropolis algorithms is an important practical problem in Markov chain Monte Carlo 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 coordinate 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 pth-order multivariate Markov process.

Article information

Source
J. Appl. Probab., Volume 50, Number 1 (2013), 1-15.

Dates
First available in Project Euclid: 20 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.jap/1363784420

Digital Object Identifier
doi:10.1239/jap/1363784420

Mathematical Reviews number (MathSciNet)
MR3076768

Zentralblatt MATH identifier
1266.60062

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 65U05

Keywords
random walk Metropolis optimal scaling optimal acceptance rate

Citation

Sherlock, Chris. Optimal scaling of the random walk Metropolis: general criteria for the 0.234 acceptance rule. J. Appl. Probab. 50 (2013), no. 1, 1--15. doi:10.1239/jap/1363784420. https://projecteuclid.org/euclid.jap/1363784420


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