Numerical Analysis for Statisticians

Every advance in computer architecture and software tempts statisticians to tackle numerically harder problems. To do so intelligently requires a good working knowledge of numerical analysis. This book is intended to equip students to craft their own software and to understand the advantages and disadvantages of different numerical methods. Issues of numerical stability, accurate approximation, computational complexity, and mathematical modeling share the limelight in a broad yet rigorous overview of those parts of numerical analysis relevant to statisticians. Although the bulk of the book covers traditional topics from linear algebra, optimization theory, numerical integration, and Fourier analysis, several chapters highlight recent statistical developments such as wavelets, the bootstrap, hidden Markov chains, and Markov chain Monte Carlo methods. These computationally intensive methods are revolutionizing statistics. Numerical Analysis for Statisticians can serve as a graduate text for either a one or a two-semester course surveying computational statistics. With a careful selection of topics and appropriate supplementation, it can even be used at the undergraduate level. It contains enough material on optimization theory alone for a one-semester graduate course. Students mastering a substantial part of the text will be well prepared for the numerical parts of advanced topics courses in statistics. Because many of the chapters nearly self-contained, professional statisticians will also find the book useful as a reference. Kenneth Lange is Professor of Biomathematics and Human Genetics at the UCLA School of Medicine. At various times during his career, he has held appointments at the University of New Hampshire, MIT, Harvard, and the University of Michigan. While at the University of Michigan, he was the Parmacia Upjohn Foundation, Professor of Biostatistics. His research interests include human genetics, population modeling, biomedical imaging, computational statistics, and applied stochastic processes. Also available by Kenneth Lange: Mathematical and Statistical Methods for Genetic Analysis, Springer-Verlag New York Inc., 1997, 265 pp., Cloth, ISBN 0-387-949097.