Approximating Integrals via Monte Carlo and Deterministic Methods

by Michael Evans, Tim Swartz

Overview

This book is designed to introduce graduate students and researchers to the primary methods useful for approximating integrals. The emphasis is on those methods that have been found to be of practical use, focusing on approximating higher- dimensional integrals with coverage of the lower-dimensional case as well. Included in the book are asymptotic techniques, multiple quadrature and quasi-random techniques and a complete development of Monte Carlo algorithms. For the Monte Carlo section important sampling methods, variance reduction techniques and the primary Markov Chain Monte Carlo algorithms are covered. This book brings these various techniques together for the first time, and provides an accessible textbook and reference for researchers in a wide variety of disciplines.

Product Details

ISBN-13:	9780198502784
Publisher:	Oxford University Press
Publication date:	06/01/2000
Series:	Oxford Statistical Science Series , #20
Edition description:	New Edition
Pages:	298
Product dimensions:	6.20(w) x 9.30(h) x 0.90(d)

About the Author

University of Toronto

Simon Fraser University

Table of Contents

1. Introduction2. Some basic concepts3. Algorithms for sampling4. Asymptotic approximations5. Multiple quadrature6. Independent importance sampling7. Markov Chain methodsReferencesAuthor indexSubject index

Editorial Reviews

"Evaluating integrals that are not known in closed form is a mathematical problem that occurs with some regularity. Although many techniques exist in the statistical and mathematical literature, a single, clearly written source of information about integral approximation has not been available. For example, there are many volumes devoted to Monte Carlo methods, but these books do not cover deterministic methods. There are numerous examples and exercises in the book, making it a self-contained resource for anyone with a solid background in advanced calculus. This volume should be required reading for graduate students in mathematical statistics and is a recommended reference for scientists whose research requires the evaluation of unknown integrals." — Richard Chechile, Journal of Mathematical Psychology, 45, 2001

"This (hardback) text is ... 'designed to introduce graduate students and researchers to the primary methods used for approximating integrals.' Topics covered include methods for sampling from standard distributions, asymptotic approximations, quadrature methods, importance sampling and Markov chain Monte Carlo (MCMC) methods. The text builds upon an earlier review paper ... and makes a valuable contribution to the area by bringing together this broad range of methods, establishing a common notation and comparing and contrasting the different approaches. ... The prose is light and very readable and the mathematics is well motivated and described, with general results presented as theorems. Thus the book is an ideal accompaniment to a relevant course as well as being an excellent reference book for those more familiar with the ideas contained therein. All in all, I would consider this book an essential addition to any library concerned with numerical integration techniques."—Biometrics

"There are few general reference books on multivariate integration, and this one helps to fill such a need. ... The book includes a number of useful examples to illustrate the theory presented."—Mathematical Reviews

From the Publisher