Uncertainty analysis with high dimensional dependence modelling. (English) Zbl 1096.62073

Kurowicka, Dorota; Cooke, Roger

Wiley Series in Probability and Statistics. Chichester: John Wiley & Sons (ISBN 0-470-86306-4/hbk; 978-0-470-86307-7/ebook). ix, 284 p. (2006).

This book is primarily concerned with the assessment of dependencies in high-dimensional distributions. The authors also discuss minimal information, diagonal band and elliptical copula. As a prerequisite it is desirable to be familiar with undergraduate analysis, statistics and probability. The book is divided into ten chapters.
Chapter 1. Introduction; Chapter 2. Assessing Uncertainty on Model Input; Chapter 3. Bivariate Dependence; Chapter 4. High-dimensional Dependence Modelling; Chapter 5. Other Graphical Models; Chapter 6. Sampling Methods; Chapter 7. Visualization; Chapter 8. Probabilistic Sensitivity Measures; Chapter 9. Probabilistic Inversion; Chapter 10. Uncertainty and the UN Compensation Commission.
There is a very good list of references. However, exercises are provided only after some selected chapters. The presentation of the new material is quite clear and it should be a useful addition to the literature on Uncertainty Analysis.

Reviewer: Arjun K. Gupta (Bowling Green)

MSC:

62H99	Multivariate analysis
62-02	Research exposition (monographs, survey articles) pertaining to statistics
62H20	Measures of association (correlation, canonical correlation, etc.)
62H05	Characterization and structure theory for multivariate probability distributions; copulas

Software:

Algorithm 647; KernSmooth