Optimal scaling of the random walk Metropolis: general criteria for the 0.234 acceptance rule. (English) Zbl 1266.60062

Summary: 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 \(p\)th-order multivariate Markov process.


60F17 Functional limit theorems; invariance principles
60J22 Computational methods in Markov chains
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