Harris recurrence of Metropolis-within-Gibbs and trans-dimensional Markov chains

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A $ϕ$-irreducible and aperiodic Markov chain with stationary probability distribution will converge to its stationary distribution from almost all starting points. The property of Harris recurrence allows us to replace ``almost all'' by ``all,'' which is potentially important when running Markov chain Monte Carlo algorithms. Full-dimensional Metropolis--Hastings algorithms are known to be Harris recurrent. In this paper, we consider conditions under which Metropolis-within-Gibbs and trans-dimensional Markov chains are or are not Harris recurrent. We present a simple but natural two-dimensional counter-example showing how Harris recurrence can fail, and also a variety of positive results which guarantee Harris recurrence. We also present some open problems. We close with a discussion of the practical implications for MCMC algorithms.
Published at http://dx.doi.org/10.1214/105051606000000510 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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Probability, 60J05 (Primary) 65C05, 60J22, 62F15 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/123978

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0702412
 http://arxiv.org/abs/math/0702412
 Annals of Applied Probability 2006, Vol. 16, No. 4, 2123-2139
 doi:10.1214/105051606000000510

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