The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 8, Number 2 (1998), 397-407.
Two convergence properties of hybrid samplers
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.
Ann. Appl. Probab., Volume 8, Number 2 (1998), 397-407.
First available in Project Euclid: 9 August 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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