The exact second eigenvalue of the Markov operator of the Gibbs sampler with random sweep strategy for Gaussian densities is calculated. A comparison lemma yields an upper bound on the second eigenvalue for bounded perturbations of Gaussians which is a significant improvement over previous bounds. For two-block Gibbs sampler algorithms with a perturbation of the form $\chi(g_1(x^{(1)}) + g_2(x^{(2)}))$ the derivative of the second eigenvalue of the algorithm is calculated exactly at $\chi = 0$, in terms of expectations of the Hessian matrices of $g_1$ and $g_2$.
Publié le : 1996-02-14
Classification:
Second eigenvalue,
Markov chains,
integral operators,
60J10,
47B38
@article{1033066202,
author = {Amit, Yali},
title = {Convergence properties of the Gibbs sampler for perturbations of Gaussians},
journal = {Ann. Statist.},
volume = {24},
number = {6},
year = {1996},
pages = { 122-140},
language = {en},
url = {http://dml.mathdoc.fr/item/1033066202}
}
Amit, Yali. Convergence properties of the Gibbs sampler for perturbations of Gaussians. Ann. Statist., Tome 24 (1996) no. 6, pp. 122-140. http://gdmltest.u-ga.fr/item/1033066202/