Preface

This book presents an introduction to fast sequential Monte Carlo (SMC) methods for counting and optimization. It is based mainly on the research work of Reuven Rubinstein and his collaborators, performed over the last ten years, on efficient Monte Carlo methods for estimation of rare-event probabilities, counting problems, and combinatorial optimization. Particular emphasis is placed on cross-entropy, minimum cross-entropy, splitting, and stochastic enumeration methods.

Our aim was to write a book on the SMC methods for a broad audience of engineers, computer scientists, mathematicians, statisticians, and, in general, anyone, theorist or practitioner, interested in efficient simulation and, in particular, efficient combinatorial optimization and counting. Our intention was to show how the SMC methods work in applications, while at the same time accentuating the unifying and novel mathematical ideas behind the SMC methods. We hope that the book stimulates further research at a postgraduate level.

The emphasis in this book is on concepts rather than on mathematical completeness. We assume that the reader has some basic mathematical background, such as a basic undergraduate course in probability and statistics. We have deliberately tried to avoid the formal “definition—lemma—theorem—proof” style of many mathematics books. Instead, we embed most definitions in the text and introduce and explain various concepts via examples and experiments.

Most of the combinatorial optimization ...

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