Daniela Gumprecht

English

Research Papers in Economics

JSS Journal of Statistical Software
September 2007, Volume 21, Book Review 3. http://www.jstatsoft.org/
Reviewer: Daniela Gumprecht
Wirtschaftsuniversit¨ at Wien
Model-based Geostatistics
Peter J. Diggle and Paulo J.Ribeiro Jr.
Springer-Verlag, New York, 2007.
ISBN 0-387-32907-2. xiii + 228 pp. USD 69.50.
http://www.leg.ufpr.br/mbgbook/
In this book statistical methods for the analysis of geostatistical data are described. Geosta-
tistical data consist of a ﬁnite sample of measured values relating to an underlying spatially
continuous phenomenon. The term model-based stands for an approach based on the appli-
cation of formal statistical methods under an explicitly assumed stochastic model.
The book is structured into three parts. The ﬁrst one (Chapters 1 and 2) gives a general
introduction and an overview of model-based geostatistics. In the second part (Chapters 3
and 4) linear and generalized linear geostatistical models are described. And the third part
(Chapters 5 to 8) deals with associated methods for the analysis of geostatistical data, where
classical as well as Bayesian approaches to parameter estimation are explained. The con-
cepts and methods are illustrated by applying them in the analysis of real data sets. Most
of these data sets can be downloaded from the book’s website. All chapters, except of Chap-
ter 8, include a computation section, where the authors show how to implement the discussed
geostatistical methods with R software and contributed packages geoR and geoRglm. Each
chapter closes with several theoretical and computational exercises.
The target audience for this book are postgraduate statistics students and scientiﬁc researchers
who are familiar with the standard tools for exploratory data analysis, regression modeling and
statistical inference. The computation sections assume that the readers know how to use R for
elementary statistics and graphics. For those who are not familiar with either the statistical
or the software premises, the authors provide helpful literature references. Furthermore, the
statistical background is summarized in the appendix.
Chapter 1 starts with some motivating examples and a description of the corresponding data
sets. Moreover, an introduction to the ﬁeld of geostatistics and some general information
about the terminology and notation, and the organization of the book are given. Chapter 2
provides an overview of model-based geostatistics. The various stages in the analysis of
geostatistical data, which range from the design to spatial estimation and prediction, are
described.
Chapter 3 deals with Gaussian models for geostatistical data, which are quite popular in prac-
tice. A Gaussian spatial process is speciﬁed by its mean function and its covariance function.2 Model-based Geostatistics
Several diﬀerent covariance functions and geostatistical models are discussed. Chapter 4 is
about generalized linear models (GLMs), which provide a unifying framework for regression
modeling of continuous or discrete data. The classical GLM is extended to accommodate
geostatistical data.
Chapter 5 discusses classical parameter estimation. The authors describe how to formulate
a suitable geostatistical model and how to estimate its parameters via least squares and
maximum likelihood. Chapter 6 concerns spatial prediction, here diﬀerent forms of kriging
are explained. Chapter 7 is about Bayesian inference. Bayesian estimation and prediction
for Gaussian linear models and generalized linear geostatistical models are presented and
illustrated in various case studies. Chapter 8 ﬁnally deals with geostatistical design, i.e.,
with the question where to locate the sample points. For diﬀerent purposes, e.g., eﬃcient
parameter estimation or spatial prediction, diﬀerent designs are optimal.
In summary, this book provides a very good insight into the ﬁeld of model-based geostatistics.
The authors succeed in getting the reader through the various stages and methods of analyzing
geostatistical data. The book can be recommended to all who are interested in model-based
approaches for the analysis of geostatistical data.
Reviewer:
Daniela Gumprecht
Department of Statistics and Mathematics
Wirtschaftsuniversit¨ at Wien
Augasse 2–6
A-1090 Wien, Austria
E-mail: Daniela.Gumprecht@wu-wien.ac.at
URL: http://statmath.wu-wien.ac.at/~gumprecht/
Journal of Statistical Software http://www.jstatsoft.org/
published by the American Statistical Association http://www.amstat.org/
Volume 21, Book Review 3 Published: 2007-09-02
September 2007

Model-based Geostatistics

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Research Papers in Economics