Approximating Integrals via Monte Carlo and Deterministic Methods (Relié)

This book is designed to introduce graduate students and researchers to the primary methods used 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, the lower-dimensional case is also covered. Included in the book are asymptotic techniques, multiple quadrature and quasi-random techniques, as well as a development of Monte Carlo algorithms. In the Monte Carlo section importance sampling methods, variance reduction techniques and Markov 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.