This book (see [Zbl 0799.62002] for the first edition from 1991) provides a comprehensive analysis of the theory and applications of spatial statistics. The author offers a unifying source of theory and methods in spatial data analysis to the scientists and the practitioners working in this field. The principle underlying his exposition is that applications drive theoretical advancements.
After an introductory chapter, the book is divided into three parts.
The first chapter gives an overview of a wide range of topics in spatial statistics, by means of several concrete examples, used as a motivation for the theory. The author divides spatial statistical data into three categories: geostatistical data, lattice data and point patterns. Spatial statistics appear, in their most essential form, as vector valued random fields \(\{ \mathbf{Z}(\mathbf{s}): \mathbf{s} \in D \}\), where \(D\) is an index set.
Part 1 is devoted to Geostatistical Data and is developed through Chapters 2 to 5. Here, the index set \(D\) is a subset of \(\mathbb{R}^n\), with non-empty interior. \(\mathbf{Z}(\mathbf{s})\) is a random vector pointed at the location \(\mathbf{s} \in D\). Therefore, this part of the book deals with spatial processes indexed over a continuous space. The main emphasis of this part is given to prediction; however, some details about estimation and hypothesis testing are given too.
Part 2 discusses Lattice Data and includes Chapters 6 and 7. Differently from Part 1, here the index set \(D\) is a discrete subset of \(\mathbb{R}^n\) and takes the form of a lattice or more generally a graph. Again, \(\mathbf{Z}(\mathbf{s})\) is a random vector at \(\mathbf{s} \in D\). Spatial processes indexed over discrete sets in space, like lattices or graphs, are the spatial analogues of time series. Chapter 6 gives conditions for which Markov random fields are well defined and identifiable, while Chapter 7 explains inferential techniques for parameters of these models.
Part 3 deals with spatial point processes, including marked point processes and random set processes. Chapter 8 is devoted to Point Patterns. Here, \(D\) is a point process in \(\mathbb{R}^n\), while \(\mathbf{Z}(\mathbf{s})\) is a random vector at the location \(\mathbf{s} \in D\). Chapter 9 is devoted to Objects. Here, \(D\) is a point process in \(\mathbb{R}^n\), while \(\mathbf{Z}(\mathbf{s})\) is a random set itself. Here, the author discusses mainly how to infer the parameters of the models from the observed point pattern.
Since its publication (see the review of the first edition in [Zbl 0799.62002]), the book became a fundamental resource for the researchers in spatial data analysis. The book is suited to scientists in many fields, but especially to researchers with a strong mathematical and statistical background. The book can be used as a reference book but also as a textbook for graduate courses. The material covered is broad and might be suitable for a period of about three semesters. The book does not contain exercises. The more mathematical oriented sections are outlined with an asterisk, while the more applied ones with a dagger.