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Convergence of Conditional Metropolis-Hastings Samplers

Part of: Markov processes Probabilistic methods, simulation and stochastic differential equations Parametric inference

Published online by Cambridge University Press:  22 February 2016

Galin L. Jones ,
Gareth O. Roberts  and
Jeffrey S. Rosenthal
Galin L. Jones*
Affiliation:
University of Minnesota
Gareth O. Roberts*
Affiliation:
University of Warwick
Jeffrey S. Rosenthal*
Affiliation:
University of Toronto
*
∗ Postal address: School of Statistics, University of Minnesota, Minneapolis, MN 55455, USA. Email address: galin@umn.edu
∗∗ Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK. Email address: gareth.o.roberts@warwick.ac.uk
∗∗∗ Postal address: Department of Statistics, University of Toronto, Toronto, Ontario, M5S 3G3, Canada. Email address: jeff@math.toronto.edu
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Abstract

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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.

Keywords

Markov chain Monte Carlo algorithmindependence samplerGibbs samplergeometric ergodicityconvergence rate

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces 60J22: Computational methods in Markov chains 65C40: Computational Markov chains 62F15: Bayesian inference
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 46 , Issue 2 , June 2014 , pp. 422 - 445
Copyright
© Applied Probability Trust 

Footnotes

Partially supported by the National Institutes for Health.

Partially supported by the Natural Sciences and Engineering Research Council of Canada.

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