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Probabilistic Divide-and-Conquer: A New Exact Simulation Method, With Integer Partitions as an Example

Published online by Cambridge University Press:  22 January 2016

RICHARD ARRATIA
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA (e-mail: rarratia@math.usc.edu)
STEPHEN DeSALVO
Affiliation:
Department of Mathematics, University of California Los Angeles, Los Angeles, CA 90024, USA (e-mail: stephendesalvo@math.ucla.edu)

Abstract

We propose a new method, probabilistic divide-and-conquer, for improving the success probability in rejection sampling. For the example of integer partitions, there is an ideal recursive scheme which improves the rejection cost from asymptotically order n3/4 to a constant. We show other examples for which a non-recursive, one-time application of probabilistic divide-and-conquer removes a substantial fraction of the rejection sampling cost.

We also present a variation of probabilistic divide-and-conquer for generating i.i.d. samples that exploits features of the coupon collector's problem, in order to obtain a cost that is sublinear in the number of samples.

Type
Paper
Copyright
Copyright © Cambridge University Press 2016 

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