Lectures on Monte Carlo Methods

Fields Institute Monographs

Neal Madras

112 pages, parution le 21/02/2003

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Résumé

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.

Contents

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

Caractéristiques techniques

	PAPIER
Éditeur(s)	American Mathematical Society (AMS)
Auteur(s)	Neal Madras
Parution	21/02/2003
Nb. de pages	112
Format	18 x 26
Couverture	Relié
Poids	427g
Intérieur	Noir et Blanc
EAN13	9780821829783
ISBN13	978-0-8218-2978-3