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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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

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

First available in Project Euclid: 20 March 2013

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

random walk Metropolis optimal scaling optimal acceptance rate


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.

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