Advances in Applied Probability

Convergence of conditional Metropolis-Hastings samplers

Galin L. Jones, Gareth O. Roberts, and Jeffrey S. Rosenthal

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Abstract

We consider Markov chain Monte Carlo algorithms which combine Gibbs updates with Metropolis-Hastings updates, resulting in a conditional Metropolis-Hastings sampler (CMH sampler). We develop conditions under which the CMH sampler will be geometrically or uniformly ergodic. We illustrate our results by analysing a CMH sampler used for drawing Bayesian inferences about the entire sample path of a diffusion process, based only upon discrete observations.

Article information

Source
Adv. in Appl. Probab., Volume 46, Number 2 (2014), 422-445.

Dates
First available in Project Euclid: 29 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.aap/1401369701

Digital Object Identifier
doi:10.1239/aap/1401369701

Mathematical Reviews number (MathSciNet)
MR3215540

Zentralblatt MATH identifier
1379.60082

Subjects
Primary: 60J05: Discrete-time Markov processes on general state spaces 60J22: Computational methods in Markov chains [See also 65C40] 65C40: Computational Markov chains 62F15: Bayesian inference

Keywords
Markov chain Monte Carlo algorithm independence sampler Gibbs sampler geometric ergodicity convergence rate

Citation

Jones, Galin L.; Roberts, Gareth O.; Rosenthal, Jeffrey S. Convergence of conditional Metropolis-Hastings samplers. Adv. in Appl. Probab. 46 (2014), no. 2, 422--445. doi:10.1239/aap/1401369701. https://projecteuclid.org/euclid.aap/1401369701


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