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Coupling and Ergodicity of Adaptive Markov Chain Monte Carlo Algorithms

Part of:Probabilistic methods, simulation and stochastic differential equationsMarkov processes

Published online by Cambridge University Press:  14 July 2016

Gareth O. Roberts and
Jeffrey S. Rosenthal
Gareth O. Roberts*
Affiliation:
Lancaster University
Jeffrey S. Rosenthal*
Affiliation:
University of Toronto
*
∗ Postal address: Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster LA1 4YF, UK. Email address: g.o.roberts@lancaster.ac.uk
∗∗ Postal address: Department of Statistics, University of Toronto, Toronto, Ontario, Canada M5S 3G3. Email address: jeff@math.toronto.edu
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Abstract

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We consider basic ergodicity properties of adaptive Markov chain Monte Carlo algorithms under minimal assumptions, using coupling constructions. We prove convergence in distribution and a weak law of large numbers. We also give counterexamples to demonstrate that the assumptions we make are not redundant.

Keywords

Markov chainscomputational methods

MSC classification

Primary:60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary:60J22: Computational methods in Markov chains65C40: Computational Markov chains

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 2 , June 2007, pp. 458 - 475
Copyright
Copyright © Applied Probability Trust 2007 

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