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E-raamat: Spatial Cluster Modelling

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Edited by (DPFM, London, UK), Edited by (University of South Carolina, Columbia, USA)
  • Formaat: 304 pages
  • Ilmumisaeg: 16-May-2002
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781420035414
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Spatial Cluster ModellingSuurem pilt
  • Formaat: 304 pages
  • Ilmumisaeg: 16-May-2002
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781420035414
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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.

Arvustused

"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

List of Contributors
xi
Preface xiii
Spatial Cluster Modelling: An Overview
1(20)
Introduction
1(2)
Historical Development
3(9)
Conventional Clustering
6(2)
Spatial Clustering
8(4)
Notation and Model Development
12(9)
Nonparametric Approaches
13(2)
Point or Object Process Modelling
15(1)
Random Effect Modelling
16(2)
Partition Modelling
18(1)
Spatio-Temporal Process Modelling
18(3)
I Point process cluster modelling 21(102)
Significance in Scale-Space for Clustering
23(14)
Introduction
23(1)
Overview
24(5)
New Method
29(6)
Future Directions
35(2)
Statistical Inference for Cox Processes
37(24)
Introduction
37(2)
Poisson Processes
39(2)
Cox Processes
41(2)
Summary Statistics
43(2)
Parametric Models of Cox Processes
45(6)
Neyman-Scott Processes as Cox Processes
45(3)
Log Gaussian Cox Processes
48(1)
Shot Noise G Cox Processes
49(2)
Estimation for Parametric Models of Cox Processes
51(3)
Prediction
54(4)
Conditional Simulation for Neyman-Scott Processes
55(1)
Conditional Simulation for LGCPs
55(1)
Conditional Simulation for Shot-noise G Cox Processes
56(2)
Discussion
58(3)
Extrapolating and Interpolating Spatial Patterns
61(26)
Introduction
61(1)
Formulation and Notation
62(4)
Germ-grain Models
63(1)
Problem Statement
63(1)
Edge Effects and Sampling Bias
64(1)
Extrapolation
65(1)
Spatial Cluster Processes
66(6)
Independent Cluster Processes
67(1)
Cox Cluster Processes
68(1)
Cluster Formation Densities
69(3)
Bayesian Cluster Analysis
72(14)
Markov Point Processes
72(2)
Sampling Bias for Independent Cluster Processes
74(1)
Spatial Birth-and-Death Processes
75(1)
Example: Redwood Seedlings
76(2)
Parameter Estimation
78(2)
Example: Cox-Matern Cluster Process
80(1)
Adaptive Coupling from the Past
80(4)
Example: Cox-Matern Cluster Process
84(2)
Summary and Conclusion
86(1)
Perfect Sampling for Point Process Cluster Modelling
87(22)
Introduction
87(2)
Bayesian Cluster Model
89(4)
Preliminaries
89(1)
Model Specification
90(3)
Sampling from the Posterior
93(2)
Specialized Examples
95(5)
Neyman-Scott Model
95(3)
Pure Silhouette Models
98(2)
Leukemia Incidence in Upstate New York
100(6)
Redwood Seedlings Data
106(3)
Bayesian Estimation and Segmentation of Spatial Point Processes Using Voronoi Tilings
109(14)
Introduction
109(1)
Proposed Solution Framework
110(2)
Formulation
110(1)
Voronoi Tilings
111(1)
Markov Chain Monte Carlo Using Dynamic Voronoi Tilings
111(1)
Intensity Estimation
112(3)
Formulation
112(1)
MCMC Implementation
112(1)
Fixed Number of Tiles
113(1)
Variable Number of Tiles
114(1)
Intensity Segmentation
115(2)
Formulation
115(1)
Fixed Number of Tiles
115(2)
Variable Number of Tiles
117(1)
Examples
117(2)
Simulated Examples
117(1)
A Sine Wave
117(1)
A Linear Feature
118(1)
New Madrid Seismic Region
118(1)
Discussion
119(4)
II Spatial process cluster modelling 123(88)
Partition Modelling
125(22)
Introduction
125(1)
Partition Models
126(9)
Partitioning for Spatial Data
127(1)
Bayesian Inference
128(3)
Predictive Inference
131(1)
Markov Chain Monte Carlo Simulation
132(1)
Partition Model Prior
133(2)
Piazza Road Dataset
135(1)
Spatial Count Data
135(9)
The Poisson-Gamma Model for Disease Mapping
137(1)
Disease Mapping with Covariates
138(3)
East German Lip Cancer Dataset
141(3)
Discussion
144(1)
Further Reading
144(3)
Cluster Modelling for Disease Rate Mapping
147(16)
Introduction
147(1)
Statistical Model
148(2)
Posterior Calculation
150(3)
Example: U.S. Cancer Mortality Atlas
153(6)
Breast Cancer
154(1)
Cervical Cancer
155(1)
Colorectal Cancer
155(4)
Lung Cancer
159(1)
Stomach Cancer
159(1)
Conclusions
159(4)
Analyzing Spatial Data Using Skew-Gaussian Processes
163(12)
Introduction
163(1)
Skew-Gaussian Processes
164(4)
The Model
165(1)
Bayesian Analysis
166(1)
Computational Strategy
167(1)
Real Data Illustration: Spatial Potential Data Prediction
168(3)
Discussion
171(4)
Accounting for Absorption Lines in Images Obtained with the Chandra X-ray Observatory
175(24)
Statistical Challenges of the Chandra X-ray Observatory
175(4)
Modeling the Image
179(5)
Model-Based Spatial Analysis
179(4)
Model-Based Spectral Analysis
183(1)
Absorption Lines
184(8)
Scientific Background
184(1)
Statistical Models
185(3)
Model Fitting
188(2)
A Simulation-Based Example
190(2)
Spectral Models with Absorption Lines
192(4)
Combining Models and Algorithms
192(3)
An Example
195(1)
Discussion
196(3)
Spatial Modelling of Count Data: A Case Study in Modelling Breeding Bird Survey Data on Large Spatial Domains
199(12)
Introduction
199(1)
The Poisson Random Effects Model
200(6)
Spectral Formulation
202(2)
Model Implementation and Prediction
204(1)
Selected Full-Conditional Distributions
205(1)
Prediction
206(1)
Implementation
206(1)
Results
206(1)
Conclusion
207(4)
III Spatio-temporal cluster modelling 211(48)
Modelling Strategies for Spatial-Temporal Data
213(14)
Introduction
213(1)
Modelling Strategy
214(1)
D-D (Drift-Drift) Models
215(5)
D-C (Drift-Correlation) Models
220(2)
C-C (Correlation-Correlation) Models
222(2)
A Unified Analysis on the Circle
224(1)
Discussion
225(2)
Spatio-Temporal Partition Modelling: An Example from Neurophysiology
227(8)
Introduction
227(1)
The Neurophysiological Experiment
227(1)
The Linear Inverse Solution
228(1)
The Mixture Model
229(3)
Initial Preparation of the Data
229(1)
Formulation of the Mixture Model
230(2)
Classification of the Inverse Solution
232(2)
Discussion
234(1)
Spatio-Temporal Cluster Modelling of Small Area Health Data
235(24)
Introduction
235(1)
Basic Cluster Modelling approaches
235(5)
Case Event Data Models
236(1)
Inter-Event versus Hidden Process Modelling
236(3)
Small Area Count Data Models
239(1)
Spatio-Temporal Extensions to Cluster Models
239(1)
A Spatio-Temporal Hidden Process Model
240(1)
Model Development
240(8)
Estimation of g(s,t)
243(1)
The Prior Distribution for Cluster Centres
244(1)
Choice of Cluster Distribution Function
245(1)
Other Prior Distributions and the Posterior Distribution
245(1)
Region Counts
246(1)
Integrated Intensity
247(1)
The Posterior Sampling Algorithm
248(1)
Goodness-of Fit Measures for the Model
249(1)
Data Example: Scottish Birth Abnormalities
249(7)
Introduction
249(1)
Exploratory Analysis
250(2)
Model Fitting Results
252(4)
Discussion
256(3)
References 259(18)
Index 277(4)
Author Index 281


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