Robert Lund
Department of Statistics
University of Georgia
"Shape-Based Converence Rates of Markov Chains"
Markov chain convergence rates have attracted much recent attention
because of the slow convergence of some Markov chain Monte Carlo sampling
algorithms. This talk studies geometric convergence issues for renewal
sequences and Markov chains; techniques for deriving good geometric
convergence rate bounds are presented. A general discussion on geometric
convergence rates of renewal sequences, which leads into the location of
roots of power series, is first presented. The methods make use of
lifetime ordering structures, e.g. decreasing hazard rate. The Markov
chain convergence rate problem is tackled for stochastically monotone
chains. Applications of the results are given.
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