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May 1998 Two convergence properties of hybrid samplers
Gareth O. Roberts, Jeffrey S. Rosenthal
Ann. Appl. Probab. 8(2): 397-407 (May 1998). DOI: 10.1214/aoap/1028903533


Theoretical work on Markov chain Monte Carlo (MCMC) algorithms has so far mainly concentrated on the properties of simple algorithms, such as the Gibbs sampler, or the full-dimensional Hastings-Metropolis algorithm. In practice, these simple algorithms are used as building blocks for more sophisticated methods, which we shall refer to as hybrid samplers. It is often hoped that good convergence properties (e.g., geometric ergodicity, etc.) of the building blocks will imply similar properties of the hybrid chains. However, little is rigorously known.

In this paper, we concentrate on two special cases of hybrid samplers. In the first case, we provide a quantitative result for the rate of convergence of the resulting hybrid chain. In the second case, concerning the combination of various Metropolis algorithms, we establish geometric ergodicity.


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Gareth O. Roberts. Jeffrey S. Rosenthal. "Two convergence properties of hybrid samplers." Ann. Appl. Probab. 8 (2) 397 - 407, May 1998.


Published: May 1998
First available in Project Euclid: 9 August 2002

zbMATH: 0938.60055
MathSciNet: MR1624941
Digital Object Identifier: 10.1214/aoap/1028903533

Primary: 60J05
Secondary: 62F99 , 62M05

Keywords: convergence rate , geometric convergence , hybrid sampler , Markov chain , Monte Carlo

Rights: Copyright © 1998 Institute of Mathematical Statistics


Vol.8 • No. 2 • May 1998
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