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Optimal Scaling of the Random Walk Metropolis: General Criteria for the 0.234 Acceptance Rule

Part of: Limit theorems

Published online by Cambridge University Press:  30 January 2018

Chris Sherlock
Chris Sherlock*
Affiliation:
Lancaster University
*
∗ Postal address: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK. Email address: c.sherlock@lancaster.ac.uk
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Abstract

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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.

Keywords

random walk Metropolisoptimal scalingoptimal acceptance rate

MSC classification

Primary: 60F17: Functional limit theorems; invariance principles
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 1 , March 2013 , pp. 1 - 15
Copyright
Copyright © Applied Probability Trust 2013 

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