Approximating Integrals via Monte Carlo and Deterministic Methods

Hardcover | April 15, 2000

byMichael Evans, Timothy Swartz

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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, and although the focus is on approximating higher- dimensional integrals thelower-dimensional case is also covered. Included in the book are asymptotic techniques, multiple quadrature and quasi-random techniques as well as a complete development of Monte Carlo algorithms. For the Monte Carlo section importance sampling methods, variance reduction techniques and the primaryMarkov Chain Monte Carlo algorithms are covered. This book brings these various techniques together for the first time, and hence provides an accessible textbook and reference for researchers in a wide variety of disciplines.

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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, and although the focus is on approximating higher- dimensional integrals thelower-dimensional case is also covered. Included in th...

Michael Evans is at University of Toronto. Timothy Swartz is at Simon Fraser University.

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Format:HardcoverDimensions:298 pages, 9.21 × 6.14 × 0.83 inPublished:April 15, 2000Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198502788

ISBN - 13:9780198502784

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Table of Contents

1. Introduction2. Some basic tools3. Algorithms for sampling from distributions4. Approximating integrals via asymptotics5. Multiple quadrature6. Importance sampling7. Markov Chain methods

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. Forexample, 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 requiredreading 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 chainMonte 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 readableand 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 inall, I would consider this bookan 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