# zbMATH — the first resource for mathematics

Computational statistics. (English) Zbl 1079.62001
Wiley Series in Probability and Statistics. Hoboken, NJ: John Wiley & Sons (ISBN 0-471-46124-5/hbk). xix, 418 p. £ 48.95 / EUR 75.00 (2005).
In this unique monograph, based on years of extensive work, the authors provide a concise and comprehensive introduction to modern computational statistics. The main goal of this book is to show how and where statistical methods work, enabling readers to apply these methods effectively.
The book is organized into three major parts: optimization (Chapters 2, 3 and 4), integration (Chapters 5, 6, 7, 8), and smoothing (Chapters 10, 11, 12). In Chapter 9 is added another essential topic, namely the bootstrap. The first part of this book introduces some optimization methods (tabu algorithms, genetic algorithms, simulated annealing, etc.) that provide very different perspectives on familiar problems. A researcher may draw ideas from such topics to design a creative and effective new algorithm.
In the second part of this book, among others, Markov chain Monte Carlo (MCMC) methods were used as methods for generating a sample from which expectations of functions $$X\sim f(x)$$ can be estimated. An application of MCMC to maximum likelihood estimation is given in this part. The third part of this book studies some methods suitable for linear smoothers. Among others, bivariate and multivariate smoothing are considered for estimating a smooth function sketched through given data. The presented smoothing algorithms are used on a variety of examples where ordinary computation techniques would fail catastrophically.
Knowledge of computer languages is not required, making examples and algorithms easier for readers to follow. The data sets for the examples are available from the book’s website. Finally, the book is ideal for all who use statistics in the workplace and in study or research including all scientists, especially in ecology, bioinformatics, medicine, computer vision, and stochastic finance.

##### MSC:
 62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics 62Pxx Applications of statistics 65C60 Computational problems in statistics (MSC2010) 62-04 Software, source code, etc. for problems pertaining to statistics 65C40 Numerical analysis or methods applied to Markov chains 62-02 Research exposition (monographs, survey articles) pertaining to statistics
##### Keywords:
computational methods in Markov chains; smoothing
Matlab; R