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Two Convergence Properties of Hybrid Samplers
Gareth O. Roberts and Jeffrey S. Rosenthal
The Annals of Applied Probability
Vol. 8, No. 2 (May, 1998), pp. 397-407
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2667307
Page Count: 11
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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.
The Annals of Applied Probability © 1998 Institute of Mathematical Statistics