This paper analyzes the Gibbs sampler applied to a standard variance component model, and considers the question of how many iterations are required for convergence. It is proved that for $K$ location parameters, with $J$ observations each, the number of iterations required for convergence (for large $K$ and $J$) is a constant times $(1 + \log K/\log J)$. This is one of the first rigorous, a priori results about time to convergence for the Gibbs sampler. A quantitative version of the theory of Harris recurrence (for Markov chains) is developed and applied.
Publié le : 1995-06-14
Classification:
Gibbs sampler,
Markov chain Monte Carlo,
rate of convergence,
variance component model,
Harris recurrence,
62M05,
60J05
@article{1176324619,
author = {Rosenthal, Jeffrey S.},
title = {Rates of Convergence for Gibbs Sampling for Variance Component Models},
journal = {Ann. Statist.},
volume = {23},
number = {6},
year = {1995},
pages = { 740-761},
language = {en},
url = {http://dml.mathdoc.fr/item/1176324619}
}
Rosenthal, Jeffrey S. Rates of Convergence for Gibbs Sampling for Variance Component Models. Ann. Statist., Tome 23 (1995) no. 6, pp. 740-761. http://gdmltest.u-ga.fr/item/1176324619/