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Simulating the Invariant Measures of Markov Chains Using Backward Coupling at Regeneration Times

Published online by Cambridge University Press:  27 July 2009

S. G. Foss ,
R. L. Tweedie  and
J. N. Corcoran
S. G. Foss
Affiliation:
Institute of Mathematics, 630090 Novosibirsk, Russia
R. L. Tweedie
Affiliation:
Department of Statistics, Colorado State University, Fort Collins, Colorado 80523
J. N. Corcoran
Affiliation:
Department of Statistics, Colorado State University, Fort Collins, Colorado 80523
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Abstract

We develop an algorithm for simulating approximate random samples from the invariant measure of a Markov chain using backward coupling of embedded regeneration times. Related methods have been used effectively for finite chains and for stochastically monotone chains: here we propose a method of implementation which avoids these restrictions by using a “cycle-length” truncation. We show that the coupling times have good theoretical properties and describe benefits and difficulties of implementing the methods in practice.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 12 , Issue 3 , July 1998 , pp. 303 - 320
Copyright
Copyright © Cambridge University Press 1998

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