Statistical Computing and Computational Statistics

Computational Statistics

by James E. Gentle

This book is evolving from notes I have used in various classes in the computational sciences (including numerical methods and computational statistics) I've taught during the past few years.

The outline is

Preface

Table of Contents

Part I. Statistical Computing: The Basics

Chapter 1. Numerical Computations and Algorithms
Chapter 2. Random Number Generation and Monte Carlo Methods
Chapter 3. Numerical Linear Algebra
Chapter 4. Nonlinear Systems, Optimization, and Robust Fitting
Chapter 5. Approximating Functions and Smoothing Data
Chapter 6. Structure in Multivariate Data
Chapter 7. Quadrature, Solution of Differential Equations, and Evaluation of Special Functions

Part II. Computationally-Intensive Methods of Statistics: Some Applications

Chapter 8. Methods of Computational Statistics
Chapter 9. Data Density
Chapter 10. Statistical Models and Fitting with Data

Appendices

Appendix A. Computer Software
Appendix B. Solutions and Hints for Selected Exercises
Appendix C. Notation and Definitions

Bibliography

Author Index

Subject Index

The book is currently over 1,300 pages. Although I am writing the book as a single document with extensive cross-references, I anticipate several volumes. Two have already appeared:

Random Number Generation and Monte Carlo Methods. This consists of Chapter 2 and some additional material on Monte Carlo studies and on software for random number generation.
Numerical Linear Algebra with Applications in Statistics. This consists of Section 1.1, Chapter 3, and some additional material on software for numerical linear algebra.

Other volumes that are in various stages of completion are

Elements of Computational Science. This consists of Chapter 1, parts of Chapters 2 through 7, Appendix A, and some additional material on numerical methods for solving differential equations. This book has no particular emphasis on statistical applications.
Optimization Methods for Statistical Applications. This consists primarily of Chapter 4 with some additional material from Chapter 5.
Elements of Computational Statistics. This consists of Chapters 8, 9, and 10; that is, Part II. Some material from Chapters 2, 3, 5, and 6 is also included.

James Gentle, jgentle@gmu.edu