Numerical Methods of Statistics

by John F. Monahan

• ISBN13: 9780521159418
• ISBN10: 0521159415
• Format: Paperback
• Copyright: 2010-09-02
• Publisher: Cambridge University Press

Summary

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. The book concludes with an examination of sorting, FFT and the application of other "fast" algorithms to statistics. Each chapter contains exercises that range in difficulty as well as examples of the methods at work. Most of the examples are accompanied by demonstration code available on a floppy disk included with the book.

Table of Contents

Algorithms and computers

Computer arithmetic

Matrices and linear equations

More methods for solving linear equations

Least squares

Eigenproblems

Functions: interpolation, smoothing and approximation

Introduction to optimization and nonlinear equations

Maximum likelihood and nonlinear regression

Numerical integration and Monte Carlo methods

Generating random variables from other distributions

Statistical methods for integration and Monte Carlo

Markov chain Monte Carlo methods

Sorting and fast algorithms

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