The Generalized Splitting method for Combinatorial Counting and Static Rare-Event Probability Estimation

Zdravko Botev (2009). The Generalized Splitting method for Combinatorial Counting and Static Rare-Event Probability Estimation PhD Thesis, School of Physical Sciences, The University of Queensland.

       
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Author Zdravko Botev
Thesis Title The Generalized Splitting method for Combinatorial Counting and Static Rare-Event Probability Estimation
School, Centre or Institute School of Physical Sciences
Institution The University of Queensland
Publication date 2009-08
Thesis type PhD Thesis
Supervisor Prof. Dirk Kroese
Dr. Joseph Grotowski
Total pages 134
Total black and white pages 134
Subjects 01 Mathematical Sciences
Abstract/Summary This thesis is divided into two parts. In the first part we describe a new Monte Carlo algorithm for the consistent and unbiased estimation of multidimensional integrals and the efficient sampling from multidimensional densities. The algorithm is inspired by the classical splitting method and can be applied to general static simulation models. We provide examples from rare-event probability estimation, counting, optimization, and sampling, demonstrating that the proposed method can outperform existing Markov chain sampling methods in terms of convergence speed and accuracy. In the second part we present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we propose a new plug-in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods. We present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability.
Keyword Static Splitting
MCMC
static rare-event probability estimation
convergence diagnostic
sequential importance sampling
Boolean Satisfiability problem
kernel density estimation
automatic bandwidth selection

 
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Created: Wed, 10 Mar 2010, 09:47:11 EST by Zdravko Botev on behalf of Library - Information Access Service