Approximating Integrals via Monte Carlo and Deterministic Methods [Hardcover]

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.

1. Introduction
2. Some basic concepts
3. Algorithms for sampling
4. Asymptotic approximations
5. Multiple quadrature
6. Independent importance sampling
7. Markov Chain methods
References
Author index
Subject index

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

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