We consider a Gibbs sampler applied to the uniform distribution on a
bounded region $R \subseteq \mathbf{R}^d$. We show that the convergence
properties of the Gibbs sampler depend greatly on the smoothness of the
boundary of R. Indeed, for sufficiently smooth boundaries the sampler is
uniformly ergodic, while for jagged boundaries the sampler could fail to even
be geometrically ergodic.
Publié le : 1998-11-14
Classification:
Gibbs sampler,
Markov chain,
Monte Carlo,
slice sampler,
uniform distribution,
curvature,
60J05,
62M05
@article{1028903381,
author = {Roberts, Gareth O. and Rosenthal, Jeffrey S.},
title = {On convergence rates of Gibbs samplers for uniform
distributions},
journal = {Ann. Appl. Probab.},
volume = {8},
number = {1},
year = {1998},
pages = { 1291-1302},
language = {en},
url = {http://dml.mathdoc.fr/item/1028903381}
}
Roberts, Gareth O.; Rosenthal, Jeffrey S. On convergence rates of Gibbs samplers for uniform
distributions. Ann. Appl. Probab., Tome 8 (1998) no. 1, pp. 1291-1302. http://gdmltest.u-ga.fr/item/1028903381/