In this paper we develop tools for analyzing the rate at which a
reversible Markov chain converges to stationarity. Our techniques are
useful when the Markov chain can be decomposed into pieces which are
themselves easier to analyze. The main theorems relate the spectral gap
of the original Markov chains to the spectral gaps of the pieces. In the
first case the pieces are restrictions of the Markov chain to subsets of
the state space; the second case treats a Metropolis--Hastings chain
whose equilibrium distribution is a weighted average of equilibrium
distributions of other Metropolis--Hastings chains on the same state
space.
Publié le : 2002-05-14
Classification:
Markov chain,
Monte Carlo,
spectral gap,
Metropolis-Hastings algorithm,
simulated tempering,
decomposition,
60J05,
65C05,
68Q25
@article{1026915617,
author = {Madras, Neal and Randall, Dana},
title = {Markov chain decomposition for convergence rate analysis},
journal = {Ann. Appl. Probab.},
volume = {12},
number = {1},
year = {2002},
pages = { 581-606},
language = {en},
url = {http://dml.mathdoc.fr/item/1026915617}
}
Madras, Neal; Randall, Dana. Markov chain decomposition for convergence rate analysis. Ann. Appl. Probab., Tome 12 (2002) no. 1, pp. 581-606. http://gdmltest.u-ga.fr/item/1026915617/