Explicit bounds for geometric convergence of Markov chains

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.