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May 2002 Markov chain decomposition for convergence rate analysis
Neal Madras, Dana Randall
Ann. Appl. Probab. 12(2): 581-606 (May 2002). DOI: 10.1214/aoap/1026915617


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.


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Neal Madras. Dana Randall. "Markov chain decomposition for convergence rate analysis." Ann. Appl. Probab. 12 (2) 581 - 606, May 2002.


Published: May 2002
First available in Project Euclid: 17 July 2002

zbMATH: 1017.60080
MathSciNet: MR1910641
Digital Object Identifier: 10.1214/aoap/1026915617

Primary: 60J05
Secondary: 65C05 , 68Q25

Keywords: Decomposition , Markov chain , Metropolis-Hastings algorithm , Monte Carlo , simulated tempering , spectral gap

Rights: Copyright © 2002 Institute of Mathematical Statistics


Vol.12 • No. 2 • May 2002
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