Spatial Cluster Modeling

This book showcases the significant advances in spatial cluster modeling since the superb account of Cressie (1993). In recent years, advances in computing power have allowed sampling from complex Bayesian models via Markov chain Monte Carlo methods such as the Gibbs and Metropolis–Hastings samplers. These advances in computing technology enable practitioners to fit complex Bayesian models (mainly hierarchical Bayesian models), not feasible in the past, to problems in spatial cluster modeling and, more generally, spatial statistics. This book focuses on the former. The book is intended for researchers and practitioners; both theory and applications are treated with equal importance. Unfortunately, no software or computer code is provided to assist practitioners with model implementation. Because of the advanced material and an absence of exercises, the book would not be appropriate for use as a textbook. Loosely, a cluster is a region where a count or reading is higher than expected. For example, one may be interested in finding regions where there is a higher-than-expected number of cases of lung cancer. Such regions are called clusters. The book describes the numerous available state-of-the-art techniques used for the definition of clusters in space (and in space-time) and the analysis of spatial cluster data. To that end, the text entertains a wide range of applications, including astrophysics, spatial epidemiology, geology, imaging, and ecology. The numerous examples are extremely useful for understanding the models and their implementation. Where possible, measure-theoretic details are avoided, enhancing readability. The text is divided into three parts. Part I addresses object and point-process modeling, Part II describes spatial process modeling, and Part III deals with spatiotemporal modeling. A brief, concise overview of traditional spatial cluster modeling techniques precedes the main text. Part I begins with significance in scale-space for clustering, which is a visual approach to locating clusters in low-dimensional space; in R1, the SiZer method is described, and in R2, the S3 method is outlined (along with a visual extension). An account of Cox point processes is followed by a description of some parametric models of Cox processes, including Neymann–Scott, log Gaussian Cox, and shot noise Gaussian Cox processes. Inference, prediction, and simulation in these models is also described. A concise delineation of extrapolation and interpolation of spatial patterns precedes a Bayesian analysis of the well-known redwood seedling dataset. An excellent exposition on the interesting problem of Bayesian landmark detection (i.e., determining whether disease clustering is centralized about some landmark representing a possible source of the disease cluster) is followed by two excellent examples. Finally, Part I concludes with Bayesian estimation and segmentation of spatial point processes. As motivated by the authors, such techniques are useful, for detecting minefields, among other phenomena. Part II introduces partition modeling, useful for allowing the correlation structure between points to vary over the sample space. In short, a partition model breaks up the sample space into disjoint regions where the data within each region are assumed to be generated by a locally parameterized model. Two illustrative examples round out the discussion. Excellent discourses on skew-Gaussian processes, disease-rate mapping, and image analysis (modeling X-ray images in astrophysics) are provided. The highlight of Part II is, I feel, an impressive chapter on modeling spatial count data, followed by a wonderful application involving bird breeding data in North America. Models used for spatiotemporal data, such as drift and correlation models, initiate Part III. Treatments of spatiotemporal partition modeling and spatiotemporal cluster modeling follow. Two examples, namely analyses of neurophysiology and Scottish birth abnormality data, highlight the aforementioned techniques. The chapter authors are all recognized for their excellence in research. Because the content focuses on new and advanced research tools, readers need a reasonable understanding of spatial cluster modeling to fully appreciate the book. With the exception of a few grammatical errors, the text is well written and informative, and is a worthy addition to the library of anyone wishing to keep up to date on current research in spatial cluster modeling.