Numerical Methods of Statistics / Edition 2

by John F. Monahan

Overview

This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available in from the author's Web site. New in this second edition are demonstrations coded in R, as well as new sections on linear programming and the Nelder-Mead search algorithm.

Product Details

ISBN-13:	9780521139519
Publisher:	Cambridge University Press
Publication date:	04/18/2011
Series:	Cambridge Series in Statistical and Probabilistic Mathematics , #32
Edition description:	New Edition
Pages:	464
Product dimensions:	7.00(w) x 9.90(h) x 1.10(d)

About the Author

John F. Monahan is a Professor of Statistics at North Carolina State University where he joined the faculty in 1978 and has been a professor since 1990. His research has appeared in numerous computational as well as statistical journals. He is also the author of A Primer on Linear Models (2008).

Table of Contents

1. Algorithms and computers; 2. Computer arithmetic; 3. Matrices and linear equations; 4. More methods for solving linear equations; 5. Least squares; 6. Eigenproblems; 7. Functions: interpolation, smoothing and approximation; 8. Introduction to optimization and nonlinear equations; 9. Maximum likelihood and nonlinear regression; 10. Numerical integration and Monte Carlo methods; 11. Generating random variables from other distributions; 12. Statistical methods for integration and Monte Carlo; 13. Markov chain Monte Carlo methods; 14. Sorting and fast algorithms.

Editorial Reviews

Review from the previous edition '... an excellent tool both for self-study and for classroom teaching. It summarizes the state of the art well and provides a solid basis, through the programs that go with the book, for numerical experimentation and further development. All in all, this is a good book to have ... I recommend it.' D. Denteneer, Mathematics of Computing

Review from the previous edition: '... this book grew out of notes for a statistical computing course ... The goal of this course was to prepare the doctoral students with the computing tools needed for statistical research. I very much liked this book and recommend it for this use.' Jaromir Antoch, Zentralblatt für Mathematik

Review from the previous edition: '... a really nice introduction to numerical analysis. All the classical subjects of a numerical analysis course are discussed in a surprisingly short and clear way ... When adapting the examples, the first half of the book can be used as a numerical analysis course for any other discipline ...' Adhemar Bultheel, Bulletin of the Belgian Mathematical Society

Review from the previous edition: '... an extremely readable book. This would be an excellent book for a graduate-level course in statistical computing.' Journal of the American Statistical Association

From the Publisher