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Lectures on Monte Carlo Methods
Neal Madras, York University, Toronto, ON, Canada
A co-publication of the AMS and Fields Institute.

Fields Institute Monographs
2002; 103 pp; hardcover
Volume: 16
ISBN-10: 0-8218-2978-5
ISBN-13: 978-0-8218-2978-3
List Price: US$36
Member Price: US$28.80
Order Code: FIM/16
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Monte Carlo methods form an experimental branch of mathematics that employs simulations driven by random number generators. These methods are often used when others fail, since they are much less sensitive to the "curse of dimensionality", which plagues deterministic methods in problems with a large number of variables. Monte Carlo methods are used in many fields: mathematics, statistics, physics, chemistry, finance, computer science, and biology, for instance.

This book is an introduction to Monte Carlo methods for anyone who would like to use these methods to study various kinds of mathematical models that arise in diverse areas of application. The book is based on lectures in a graduate course given by the author. It examines theoretical properties of Monte Carlo methods as well as practical issues concerning their computer implementation and statistical analysis. The only formal prerequisite is an undergraduate course in probability.

The book is intended to be accessible to students from a wide range of scientific backgrounds. Rather than being a detailed treatise, it covers the key topics of Monte Carlo methods to the depth necessary for a researcher to design, implement, and analyze a full Monte Carlo study of a mathematical or scientific problem. The ideas are illustrated with diverse running examples. There are exercises sprinkled throughout the text. The topics covered include computer generation of random variables, techniques and examples for variance reduction of Monte Carlo estimates, Markov chain Monte Carlo, and statistical analysis of Monte Carlo output.

Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).


Advanced undergraduates, graduate students, research mathematicians, statisticians, physicists, chemists, engineers, and computer scientists interested in numerical analysis, probability theory, and stochastic processes.


"Short but enlightening introduction to the subject ... ideal text for a first graduate course on Monte Carlo methods for statisticians, mathematicians, computer scientists, and other scientists. The author is a leading expert in the field and he has made a careful choice of material to give readers a good basic introduction to the field."

-- CMS Notes

Table of Contents

  • Introduction
  • Generating random numbers
  • Variance reduction techniques
  • Markov chain Monte Carlo
  • Statistical analysis of simulation output
  • The Ising model and related examples
  • Bibliography
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