Statistics for Spatial Data

This is the second edition of the leading text on the characterization and analysis of data collected at different points of space. It was written as the text for a course, but it also serves as an encyclopedic guide to the subject. It is aimed primarily at scientists and engineers. The author sees his task as “taking the diverse and uneven literature on spatial statistics and extending it, correcting it and unifying it”. He comments that this has not been an easy task.

The author explores three primary categories of spatial data: geostatistical data, lattice data, and point pattern data. These are general groupings with soft boundaries between them, but they serve to create some useful distinctions. The categories are distinguished largely by the types of observations that they consider. Geostatistics works with data that have variability at both large and small scale, and so is often concerned with modeling spatial trend and spatial correlation. Lattice data arise when data are gathered at regular or irregular locations in space that have links to other locations. The links could be nearest-neighbor-like links or links that are associational rather than distance-related. Point patterns concern data that characterize the location of events.

The three types of data arise in an amazing variety of applications. Geostatistical data naturally arises in applications dealing with geology, mining, soil science, water usage, and crop yield. Lattice data is a natural way to interpret information from remote sensing, image analysis, or regional mapping designed to identify, for example, local clusters of disease outbreak. Point patterns occurs in fields such as archeology, cosmology, geography and seismology. The author presents an extended example of a point pattern analysis of the distribution of longleaf-pines in one county in Georgia that shows some unusual clustering.

Each of the chapters and sections of the book are marked to indicate whether they deal primarily with theory or with applications. The author suggests that the application-oriented sections should be broadly accessible to people with a basic background in statistics. Most chapters begin with an application, a kind of gentle invitation to read on. The remainder of the book is accessible at different levels requiring varying degrees of mathematical and statistical backgrounds. The most advanced material — approaching research frontiers — deals with random processes, point processes and random sets.

Most of the theoretical parts of the book deal with analysis and characterization of data, modeling and prediction. Especially notable is the author’s extensive treatment of “kriging” (optimal prediction) for making inferences about unobserved values of a random process based on observations at certain spatial locations with the unknown values modeled by a Gaussian process controlled by prior covariances. This is a tool widely used in geostatistics. Markov processes are also an essential tool — especially Markov random fields and Markov point processes.

The author’s treatment of the subject is so comprehensive that it could likely overwhelm the reader, especially one new to the field. The author’s suggestion for less sophisticated readers to approach the text through applications is a good one.

Bill Satzer (bsatzer@gmail.com) was a senior intellectual property scientist at 3M Company. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.