The Annals of Applied Probability

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

Mylène Bédard

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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.

Article information

Ann. Appl. Probab. Volume 17, Number 4 (2007), 1222-1244.

First available in Project Euclid: 10 August 2007

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems
Secondary: 65C40: Computational Markov chains

Metropolis algorithm weak convergence optimal scaling diffusion Markov chain Monte Carlo


Bédard, Mylène. Weak convergence of Metropolis algorithms for non-i.i.d. target distributions. Ann. Appl. Probab. 17 (2007), no. 4, 1222--1244. doi:10.1214/105051607000000096.

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