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Explicit bounds for geometric convergence of Markov chains

Part of: Markov processes Distribution theory

Published online by Cambridge University Press:  14 July 2016

John E. Kolassa
John E. Kolassa*
Affiliation:
University of Rochester Medical Center
*
∗Postal address: Department of Statistics, Rutgers University, 501 Hill Center, Bush Campus, Piscataway, NJ 08855 USA. Email address: kolassa@stat.rutgers.edu
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Abstract

This paper presents bounds on convergence rates of Markov chains in terms of quantities calculable directly from chain transition operators. Bounds are constructed by creating a probability distribution that minorizes the transition kernel over some region, and by examining bounds on an expectation conditional on lying within and without this region. These are shown to be sharper in most cases than previous similar results. These bounds are applied to a Markov chain useful in frequentist conditional inference in canonical generalized linear models.

Keywords

Markov Chain Monte Carlogeometric convergence

MSC classification

Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Secondary: 62E20: Asymptotic distribution theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 3 , September 2000 , pp. 642 - 651
Copyright
Copyright © Applied Probability Trust 2000 

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