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.
Publié le : 2007-08-14
Classification:
Metropolis algorithm,
weak convergence,
optimal scaling,
diffusion,
Markov chain Monte Carlo,
60F05,
65C40
@article{1186755238,
author = {B\'edard, Myl\`ene},
title = {Weak convergence of Metropolis algorithms for non-i.i.d. target distributions},
journal = {Ann. Appl. Probab.},
volume = {17},
number = {1},
year = {2007},
pages = { 1222-1244},
language = {en},
url = {http://dml.mathdoc.fr/item/1186755238}
}
Bédard, Mylène. Weak convergence of Metropolis algorithms for non-i.i.d. target distributions. Ann. Appl. Probab., Tome 17 (2007) no. 1, pp. 1222-1244. http://gdmltest.u-ga.fr/item/1186755238/