The Annals of Applied Probability

Two convergence properties of hybrid samplers

Gareth O. Roberts and Jeffrey S. Rosenthal

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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.

Article information

Ann. Appl. Probab., Volume 8, Number 2 (1998), 397-407.

First available in Project Euclid: 9 August 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 62F99: None of the above, but in this section 62M05: Markov processes: estimation

Markov chain Monte Carlo hybrid sampler geometric convergence convergence rate


Roberts, Gareth O.; Rosenthal, Jeffrey S. Two convergence properties of hybrid samplers. Ann. Appl. Probab. 8 (1998), no. 2, 397--407. doi:10.1214/aoap/1028903533.

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