Speeding up the FMMR perfect sampling algorithm: A case study revisited

Authors

  • Robert P. Dobrow,

    1. Mathematics and Computer Science Department, Carleton College, Northfield, Minnesota 55057
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  • James Allen Fill

    Corresponding author
    1. Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, Maryland 21218-2682
    • Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, Maryland 21218-2682
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    • *

      Research for this author supported by NSF Grants DMS-9803780 and DMS-0104167, and for both authors by The Johns Hopkins University's Acheson J. Duncan Fund for the Advancement of Research in Statistics.


Abstract

In a previous paper by the second author, two Markov chain Monte Carlo perfect sampling algorithms—one called coupling from the past (CFTP) and the other (FMMR) based on rejection sampling—are compared using as a case study the move-to-front (MTF) self-organizing list chain. Here we revisit that case study and, in particular, exploit the dependence of FMMR on the user-chosen initial state. We give a stochastic monotonicity result for the running time of FMMR applied to MTF and thus identify the initial state that gives the stochastically smallest running time; by contrast, the initial state used in the previous study gives the stochastically largest running time. By changing from worst choice to best choice of initial state we achieve remarkable speedup of FMMR for MTF; for example, we reduce the running time (as measured in Markov chain steps) from exponential in the length n of the list nearly down to n when the items in the list are requested according to a geometric distribution. For this same example, the running time for CFTP grows exponentially in n. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2003

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