Weak convergence of Metropolis algorithms for non-i.i.d. target distributions

Open Access

1 August 2007

journal article
Published by Institute of Mathematical Statistics in The Annals of Applied Probability

Vol. 17 (4) , 1222-1244
https://doi.org/10.1214/105051607000000096

Abstract

In this paper, we shall optimize the efficiency of Metropolis algorithms for multidimensional target distributions with scaling terms possibly depending on the dimension. We propose a method for determining the appropriate form for the scaling of the proposal distribution as a function of the dimension, which leads to the proof of an asymptotic diffusion theorem. We show that when there does not exist any component with a scaling term significantly smaller than the others, the asymptotically optimal acceptance rate is the well-known 0.234.

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