## The Annals of Applied Probability

### Two convergence properties of hybrid samplers

#### Abstract

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

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

Dates
First available in Project Euclid: 9 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1028903533

Digital Object Identifier
doi:10.1214/aoap/1028903533

Mathematical Reviews number (MathSciNet)
MR1624941

Zentralblatt MATH identifier
0938.60055

#### Citation

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. https://projecteuclid.org/euclid.aoap/1028903533

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