Spatial Cluster Modelling

Spatial clustering is a topic of growing interest in many disciplines, from geoscience to epidemiology. In recent years, many new advances have appeared, particularly in the area of Bayesian cluster modelling. However, much of this work has been scattered in disparate areas of the literature. This book provides, in one integrated volume, a review of the state-of-the-art in spatial clustering and spatial cluster modelling. Organized in three sections, it includes an overview of the field and its applications, discussions of the theoretical underpinnings of methodology, and explorations of spatio-temporal cluster modelling, all written by leading researchers in the field.

Research has generated a number of advances in methods for spatial cluster modelling in recent years, particularly in the area of Bayesian cluster modelling. Along with these advances has come an explosion of interest in the potential applications of this work, especially in epidemiology and genome research. In one integrated volume, this book reviews the state-of-the-art in spatial clustering and spatial cluster modelling, bringing together research and applications previously scattered throughout the literature. It begins with an overview of the field, then presents a series of chapters that illuminate the nature and purpose of cluster modelling within different application areas, including astrophysics, epidemiology, ecology, and imaging. The focus then shifts to methods, with discussions on point and object process modelling, perfect sampling of cluster processes, partitioning in space and space-time, spatial and spatio-temporal process modelling, nonparametric methods for clustering, and spatio-temporal cluster modelling. Many figures, some in full color, complement the text, and a single section of references cited makes it easy to locate source material. Leading specialists in the field of cluster modelling authored each chapter, and an introduction by the editors to each chapter provides a cohesion not typically found in contributed works. Spatial Cluster Modelling thus offers a singular opportunity to explore this exciting new field, understand its techniques, and apply them in your own research.

SPATIAL CLUSTER MODELLING: AN OVERVIEWIntroduction Historical Development Notation and Model Development I. POINT PROCESS CLUSTER MODELLING SIGNIFICANCE IN SCALE-SPACE FOR CLUSTERING Introduction Overview New Method Future Directions STATISTICAL INFERENCE FOR COX PROCESSES Introduction Poisson Processes Cox Processes Summary Statistics Parametric Models of Cox Processes Estimation for Parametric Models of Cox Processes Prediction Discussion EXTRAPOLATING AND INTERPOLATING SPATIAL PATTERNS Introduction Formulation and Notation Spatial Cluster Processes Bayesian Cluster Analysis Summary and Conclusion PERFECT SAMPLING FOR POINT PROCESS CLUSTER MODELLING Introduction Bayesian Cluster Model Sampling from the Posterior Specialized Examples Leukemia Incidence in Upstate New York Redwood Seedlings Data BAYESIAN ESTIMATION AND SEGMENTATION OF SPATIAL POINT PROCESSES USING VORONOI TILINGSIntroduction Proposed Solution Framework Intensity Estimation Intensity Segmentation Examples Discussion II. SPATIAL PROCESS CLUSTER MODELLING PARTITION MODELLING Introduction Partition Models Piazza Road Dataset Spatial Count Data Discussion Further Reading CLUSTER MODELLING FOR DISEASE RATE MAPPING Introduction Statistical Model Posterior Calculation Example: U.S. Cancer Mortality Atlas Conclusions ANALYZING SPATIAL DATA USING SKEW-GAUSSIAN PROCESSES Introduction Skew-Gaussian Processes Real Data Illustration: Spatial Potential Data Prediction Discussion ACCOUNTING FOR ABSORPTION LINES IN IMAGES OBTAINED WITH THE CHANDRA X-RAY OBSERVATORY Statistical Challenges of the Chandra X-Ray Observatory Modeling the Image Absorption Lines Spectral Models with Absorption Lines Discussion SPATIAL MODELLING OF COUNT DATA: A CASE STUDY IN MODELLING BREEDING BIRD SURVEY DATA ON LARGE SPATIAL DOMAINS Introduction The Poisson Random Effects Model Results Conclusion III. SPATIO-TEMPORAL CLUSTER MODELLING MODELLING STRATEGIES FOR SPATIAL-TEMPORAL DATA Introduction Modelling Strategy D-D (Drift-Drift) Models D-C (Drift-Correlation) Models C-C (Correlation-Correlation) Models A Unified Analysis on the Circle Discussion SPATIO-TEMPORAL PARTITION MODELLING: AN EXAMPLE FROM NEUROPHYSIOLOGY Introduction The Neurophysiological Experiment The Linear Inverse Solution The Mixture Model Classification of the Inverse Solution Discussion SPATIO-TEMPORAL CLUSTER MODELLING OF SMALL AREA HEALTH DATA Introduction Basic Cluster Modelling Approaches A Spatio-Temporal Hidden Process Model Model Development The Posterior Sampling Algorithm Data Example: Scottish Birth Abnormalities Discussion REFERENCES INDEX AUTHOR INDEX

Lawson\, Andrew B.; Denison\, David G.T.