Spatial Cluster Modelling: 1st Edition (Hardback) book cover

Spatial Cluster Modelling

1st Edition

Edited by Andrew B. Lawson, David G.T. Denison

Chapman and Hall/CRC

304 pages | 9 Color Illus. | 60 B/W Illus.

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pub: 2002-05-16
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Description

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.

Reviews

"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

Table of Contents

SPATIAL CLUSTER MODELLING: AN OVERVIEW

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

About the Authors/Editors

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

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General