The design and analysis of computer experiments. (English) Zbl 1041.62068

Santner, Thomas J.; Williams, Brian J.; Notz, William I.

Springer Series in Statistics. New York, NY: Springer (ISBN 0-387-95420-1/hbk). xii, 283 p. (2003).

This book is devoted to applied statistics, the theory that explores ways of estimating functional dependency from a given collection of data. This problem covers important topics of classical statistics – in particular, prediction methodology for computer experiments, designs based on methods for selecting random samples, sensitivity analysis and model validation, etc. The book is organized as follows.
Chapter 2 begins by considering the design and analysis of computer experiments. This includes a classification of the types of input variables and an introduction to Gaussian random field models as a description of the output from a computer experiment. Chapter 3 describes methods that can be used for predicting the output of computer codes based on training data. Chapter 4 considers several additional topics, including the use of predictive distributions and prediction based on multiple outputs. Chapter 5 gives an overview of space-filling designs, such as: designs generated by elementary methods for selecting samples, designs generated by latin hypercube sampling, designs based on measures of distance, etc. Chapter 6 discusses designs based on statistical criteria (maximum entropy and mean squared error of prediction). Finally, Chapter 7 concerns some issues of validation of computer experiments using sensitivity analysis based on regression modeling, ANOVA-type decompositions, etc.
The book is intended as a textbook for a graduate course of statistics. The students and practitioners should be familiar with designing, modeling and analyzing computer experiments. Slightly more elaborate models are analyzed by means of the PErK software, written in C and freely available by readers.

Reviewer: J. Martyna (Kraków)

MSC:

62K99	Design of statistical experiments
62-02	Research exposition (monographs, survey articles) pertaining to statistics
68U07	Computer science aspects of computer-aided design
62K20	Response surface designs

Keywords:

research exposition