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.
Introduction
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 TILINGS
Introduction
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
Biography
Andrew B. Lawson, David G.T. Denison
"This text provides an effective treatment and review of several ways to view a clustering pattern, depending on the context. Examples include image segmentation, spatial epidemiology, and object recognition using partition models. … Each of the 14 chapters has multiple authors, each aware of the book's content so there is effective cross-referencing. I strongly recommend this book for anybody who is serious about spatial clustering. …"
-Tom Burr Statistics in Medicine, Vol. 23, 2004
"[This book] is a collection of contributions by leading specialist in the field, which are brought together coherently with unified notation. … Overall, the book is an excellent, well and up-to-date referenced presentation of the current state of research in spatial cluster analysis … an insightful reference not only for the statistician, but also for scientists … ."
-Zentralblatt MATH, 1046
"The chapter authors are all recognized for their excellence in research. … 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."
-Journal of the American Statistical Association, Vol. 99, No. 467, September 2004
