Numerical Methods of Statistics

This second edition explains how computer software is designed to perform the tasks required for sophisticated statistical analysis.

John F. Monahan (Author)

9780521191586, Cambridge University Press

Hardback, published 18 April 2011

464 pages
25.4 x 17.8 x 2.5 cm, 1.02 kg

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

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 from the author's website. New in this second edition are demonstrations coded in R, as well as new sections on linear programming and the Nelder–Mead search algorithm.

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.

Subject Areas: Machine learning [UYQM], Probability & statistics [PBT], Numerical analysis [PBKS]