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

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.

Published in at http://dx.doi.org/10.1214/105051607000000096 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• General state space Markov chains and MCMC algorithms
• Optimal scaling for partially updating MCMC algorithms
• Optimal Scaling of Mala for Nonlinear Regression

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