This discussion paper resulted in a publication in <Stochastic Models</I> (2012). Volume 28(3), pages 478-502.<P> We apply the splitting method to three well-known counting problems, namely 3-SAT, random graphs with prescribed degrees, and binary contingency tables. We present an enhanced version of the splitting method...</p></stochastic>

The Cross Entropy method is a well-known adaptive importance sampling method for rare-event probability estimation, which requires estimating an optimal importance sampling density within a parametric class. In this article we estimate an optimal importance sampling density within a wider...

In this paper we describe a Sequential Importance Sampling (SIS) procedure for counting the number of vertex covers in general graphs. The performance of SIS depends heavily on how close the SIS proposal distribution is to a uniform one over a suitably restricted set. The proposed algorithm...