Explicit bounds for geometric convergence of Markov chains

This paper presents bounds on convergence rates of Markov chains in terms o f quantities calculable directly from chain transition operators. Bounds ar e constructed by creating a probability distribution that minorizes the tra nsition 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 cares than previous similar results. These bounds are appli ed to a Markov chain useful in frequentist conditional inference in canonic al generalized linear models.