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Explicit bounds for geometric convergence of Markov chains

Published online by Cambridge University Press:  14 July 2016

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

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2000 

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