Convergence of conditional metropolis-hastings samplers

Galin L. Jones; Gareth O. Roberts; Jeffrey S. Rosenthal

doi:10.1239/aap/1401369701

Convergence of conditional metropolis-hastings samplers

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

Statistics (Twin Cities)

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

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 aCMHsampler used for drawing Bayesian inferences about the entire sample path of a diffusion process, based only upon discrete observations.

Original language	English (US)
Pages (from-to)	422-445
Number of pages	24
Journal	Advances in Applied Probability
Volume	46
Issue number	2
DOIs	https://doi.org/10.1239/aap/1401369701
State	Published - Jun 2014

Keywords

Convergence rate
Geometric ergodicity
Gibbs sampler
Independence sampler
Markov chain Monte Carlo algorithm

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10.1239/aap/1401369701

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AU - Roberts, Gareth O.

AU - Rosenthal, Jeffrey S.

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AB - 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 aCMHsampler used for drawing Bayesian inferences about the entire sample path of a diffusion process, based only upon discrete observations.

KW - Convergence rate

KW - Geometric ergodicity

KW - Gibbs sampler

KW - Independence sampler

KW - Markov chain Monte Carlo algorithm

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Convergence of conditional metropolis-hastings samplers

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