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

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

2007-10-19

arxiv.org/abs/0710.3684v1

Annals of Applied Probability 2007, Vol. 17, No. 4, 1222-1244

Mathematics

Probability

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

Scientific paper

10.1214/105051607000000096

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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