An Introduction to Statistical Modeling of Extreme Values
by Stuart Coles
Description
Directly oriented towards real practical application, this book develops the basic theoretical framework of extreme value models and the statistical inference techniques for using these models in practice.
Intended for statisticians and non-statisticians alike, the theoretical treatment is elementary, with heuristics often replacing detailed mathematical proof. Most aspects of extreme modeling techniques are covered, including historical techniques (still widely used) and contemporary techniques based on point process models. A wide range of worked examples, using genuine datasets, illustrate the various modeling procedures and a concluding chapter provides a brief intorduction to a number of more advanced topics, including Bayesian inference and spatial extremes.
All the computations are carried out using S-PLUS, and the corresponding datasets and functions are available via the internet for readers to recreate examples for themselves. An essential reference for students and researchers in statistics and disciplines such as engineering, finance and environmental science, this book will also appeal to practicioners looking for practical help in solving real problems.
Stuart Coles is Reader in Statistics at the University of Bristol, U.K., having previously lectured at the universities of Nottingham and Lancaster. In 1992 he was the first recipient of the Royal Statistical Society's research prize. He has published widely in the statistical literature, principally in the area of extreme value modeling.
As recommended by Robert I. Willows in his email to the AIACC discussion list:
I would only add that in (albeit unlikley) circumstances where one does have the benefit of historical data sets of sufficient length that one is tempted to use them to estimate the probability or frequency associated with particular extreme values, that conventional statistical approaches, based on assumptions of normal (or other similar)
distribution of data and errors, do not lead to robust estimates. Most of the dataset effectively provides little information on the tail.
Better approaches are based on extreme value theory and the use of particular pdf's to model the distribution of extreme values. I particularly recommend the recent book by Suart Coles. In particular his case study of flooding in Peru is interesting it even manages to distinguish a recent flood event as an outlier (indicating influence of
climate change ?) given the historical distribution of extreme rainfall events.
The reference is included in the Climate adaptation: Risk, Uncertainty and decision-makingguidance document I circulated at the recent workshop in Trieste.
The following web address gives details of Stuart's book and incl. S-plus routines to fit extreme value pdf's to suitable datasets.
In principle, I imagine that the techniqes could be applied to describe the extreme values output from GCM's or RCM's, but accepting that the estimates are conditioned by the averaging inherent to the climate model output.