Theory of Spatial Statistics: A Concise Introduction presents the most important models used in spatial statistics, including random fields and point processes, from a rigorous mathematical point of view and shows how to carry out statistical inference. It contains full proofs, real-life examples and theoretical exercises. Solutions to the latter are available in an appendix.
Assuming maturity in probability and statistics, these concise lecture notes are self-contained and cover enough material for a semester course. They may also serve as a reference book for researchers.
* Presents the mathematical foundations of spatial statistics.
* Contains worked examples from mining, disease mapping, forestry, soil and environmental science, and criminology.
* Gives pointers to the literature to facilitate further study.
* Provides example code in R to encourage the student to experiment.
* Offers exercises and their solutions to test and deepen understanding.
The book is suitable for postgraduate and advanced undergraduate students in mathematics and statistics.
Table of Contents
Random field modelling and interpolation
Models and inference for areal unit data
Spatial point processes
Appendix: Solutions to theoretical exercises
Marie-Colette van Lieshout is a Researcher in the group Stochastics of the Centre for Mathematics and Computer Science CWI and at the University Twente.
"This book provides a concise and readable introduction to the three main areas of spatial statistics: random fields, areal data and spatial point processes. Although the focus is on the basic underlying theory, extensive analyses of real data are provided including R code. Suitable as a text or for self-study, each major chapter includes exercises and solutions. A valuable resource for students and researchers in statistics and related fields looking to learn some of the basic theory underlying spatial statistics."
- Michael Stein, University of Chicago
"The book is a concise introduction to spatial statistics mostly from a mathematical point of view. It devotes a chapter to each of the main classes of spatial statistics settings, point referenced data and interpolation, areal data and spatial point processes. Each chapter contain all the main definitions and theorem (with proofs) for relevant models, and some of the inference methods for each of these spatial statistics settings. The chapters end with worked through R-examples and nice and useful pointers to the literature. The book expect the reader to be both mathematical and statistical mature, and most examples are mathematical. I think this can be a nice introduction and reference book for PhD students specializing in spatial statics, and it can also work as a supporting textbook for a mathematically orientated master level course in spatial statistics."
- Ingelin Steinsland, Norwegian University of Science and Technology
"Theory of Spatial Statistics: A Concise Introduction is an excellent introductory resource to all three subfields in spatial statistics: geostatistics, areal data, and point processes. The book is well-organized and self-contained, covering the key knowledge of spatial statistics in a unified manner. It describes the mathematical foundations of the related statistical theory with rigorous proofs. Each chapter contains detailed illustrative examples using R packages to exemplify the methodologies applied to some well-known data sets. The book is suitable as a textbook for both graduate and advanced undergraduate students who want to learn the basis of the fast-growing areas of spatial statistics. I like the idea of providing exercises and detailed solutions so that readers can assess their learning outcomes. This book will also be of interest to practitioners of applied statistics from various disciplines as a reference book."
- Yang Li, University of Minnesota Duluth
"This text provides an excellent introduction to spatial statistics, including some important theoretical results, as well as practical implementation of the methodologies discussed. The modeling approaches are naturally separated into three groups depending on the type of data at hand, i.e., gridded, area unit and mapped point pattern data. The author has managed to incorporate in the text the most commonly used approaches in the literature, along with their corresponding applications. One particularly useful feature is the illustration of R packages to fit these models. Moreover, the inclusion of solutions to theoretical problems offers a nice resource to refer to and utilize in teaching graduate courses on spatial statistics and point processes. In addition, the theoretical results presented make for a nice blend between theory and application. Overall, the book is well written and will be a welcomed addition to the library of any researcher in spatial statistics."
- Athanasios (Sakis) Christou Micheas, University of Missouri-Columbia
"This book surveys the main topics in spatial statistics, including modeling random fields, variogram estimation, hierarchical models, and spatial point processes...It is amazing how much information van Lieshout is able to convey so concisely and compactly. She is simply masterful at explaining very difficult, intricate, and important concepts, models and statistical methods in an eloquent way...The chapters are wonderfully well organized and cover an ideal list of core topics in the statistical analysis of the most common and important forms of spatial data. Perhaps the best part of the book are the worked examples, which aid the reader new to this material and help crystalize what these statistical models and methods are prescribing...It is clear that an enormous amount of effort went into these worked examples, though as with the theoretical topics, van Lieshout explains everything so clearly and concisely that she makes the applications and R coding look easy, and in some cases almost trivial...(The book) is a remarkable fusion of the most important topics in the field, both theoretical and applied, presented beautifully and eloquently with the utmost care and precision, and so concisely that it all fits into a small handbook. I would strongly recommend this book for anyone teaching a one-semester graduate level course in spatial statistics."
- Frederic P. Schoenberg, University of California at Los Angeles