Spatial cluster modelling

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Publication Information:

Boca Raton, Fla. : Chapman & Hall/CRC, 2002

ISBN:

9781584882664

Subject Term:

Cluster analysis

Spatial analysis (Statistics)

Added Author:

Lawson, Andrew (Andrew B.)

Denison, David G. T.

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Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010029168	QA278 L39 2002	Open Access Book	Book	Searching... Unknown

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.

Author Notes

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

List of Contributors	p. xi
Preface	p. xiii
1 Spatial Cluster Modelling: An Overview	p. 1
1.1 Introduction	p. 1
1.2 Historical Development	p. 3
1.2.1 Conventional Clustering	p. 6
1.2.2 Spatial Clustering	p. 8
1.3 Notation and Model Development	p. 12
1.3.1 Nonparametric Approaches	p. 13
1.3.2 Point or Object Process Modelling	p. 15
1.3.3 Random Effect Modelling	p. 16
1.3.4 Partition Modelling	p. 18
1.3.5 Spatio-Temporal Process Modelling	p. 18
I Point process cluster modelling	p. 21
2 Significance in Scale-Space for Clustering	p. 23
2.1 Introduction	p. 23
2.2 Overview	p. 24
2.3 New Method	p. 29
2.4 Future Directions	p. 35
3 Statistical Inference for Cox Processes	p. 37
3.1 Introduction	p. 37
3.2 Poisson Processes	p. 39
3.3 Cox Processes	p. 41
3.4 Summary Statistics	p. 43
3.5 Parametric Models of Cox Processes	p. 45
3.5.1 Neyman-Scott Processes as Cox Processes	p. 45
3.5.2 Log Gaussian Cox Processes	p. 48
3.5.3 Shot Noise G Cox Processes	p. 49
3.6 Estimation for Parametric Models of Cox Processes	p. 51
3.7 Prediction	p. 54
3.7.1 Conditional Simulation for Neyman-Scott Processes	p. 55
3.7.2 Conditional Simulation for LGCPs	p. 55
3.7.3 Conditional Simulation for Shot-noise G Cox Processes	p. 56
3.8 Discussion	p. 58
4 Extrapolating and Interpolating Spatial Patterns	p. 61
4.1 Introduction	p. 61
4.2 Formulation and Notation	p. 62
4.2.1 Germ-grain Models	p. 63
4.2.2 Problem Statement	p. 63
4.2.3 Edge Effects and Sampling Bias	p. 64
4.2.4 Extrapolation	p. 65
4.3 Spatial Cluster Processes	p. 66
4.3.1 Independent Cluster Processes	p. 67
4.3.2 Cox Cluster Processes	p. 68
4.3.3 Cluster Formation Densities	p. 69
4.4 Bayesian Cluster Analysis	p. 72
4.4.1 Markov Point Processes	p. 72
4.4.2 Sampling Bias for Independent Cluster Processes	p. 74
4.4.3 Spatial Birth-and-Death Processes	p. 75
Example: Redwood Seedlings	p. 76
4.4.4 Parameter Estimation	p. 78
Example: Cox-Matern Cluster Process	p. 80
4.4.5 Adaptive Coupling from the Past	p. 80
4.4.6 Example: Cox-Matern Cluster Process	p. 84
4.5 Summary and Conclusion	p. 86
5 Perfect Sampling for Point Process Cluster Modelling	p. 87
5.1 Introduction	p. 87
5.2 Bayesian Cluster Model	p. 89
5.2.1 Preliminaries	p. 89
5.2.2 Model Specification	p. 90
5.3 Sampling from the Posterior	p. 93
5.4 Specialized Examples	p. 95
5.4.1 Neyman-Scott Model	p. 95
5.4.2 Pure Silhouette Models	p. 98
5.5 Leukemia Incidence in Upstate New York	p. 100
5.6 Redwood Seedlings Data	p. 106
6 Bayesian Estimation and Segmentation of Spatial Point Processes Using Voronoi Tilings	p. 109
6.1 Introduction	p. 109
6.2 Proposed Solution Framework	p. 110
6.2.1 Formulation	p. 110
6.2.2 Voronoi Tilings	p. 111
6.2.3 Markov Chain Monte Carlo Using Dynamic Voronoi Tilings	p. 111
6.3 Intensity Estimation	p. 112
6.3.1 Formulation	p. 112
6.3.2 MCMC Implementation	p. 112
Fixed Number of Tiles	p. 113
Variable Number of Tiles	p. 114
6.4 Intensity Segmentation	p. 115
6.4.1 Formulation	p. 115
Fixed Number of Tiles	p. 115
Variable Number of Tiles	p. 117
6.5 Examples	p. 117
6.5.1 Simulated Examples	p. 117
A Sine Wave	p. 117
A Linear Feature	p. 118
6.5.2 New Madrid Seismic Region	p. 118
6.6 Discussion	p. 119
II Spatial process cluster modelling	p. 123
7 Partition Modelling	p. 125
7.1 Introduction	p. 125
7.2 Partition Models	p. 126
7.2.1 Partitioning for Spatial Data	p. 127
7.2.2 Bayesian Inference	p. 128
7.2.3 Predictive Inference	p. 131
7.2.4 Markov Chain Monte Carlo Simulation	p. 132
7.2.5 Partition Model Prior	p. 133
7.3 Piazza Road Dataset	p. 135
7.4 Spatial Count Data	p. 135
7.4.1 The Poisson-Gamma Model for Disease Mapping	p. 137
7.4.2 Disease Mapping with Covariates	p. 138
7.4.3 East German Lip Cancer Dataset	p. 141
7.5 Discussion	p. 144
7.6 Further Reading	p. 144
8 Cluster Modelling for Disease Rate Mapping	p. 147
8.1 Introduction	p. 147
8.2 Statistical Model	p. 148
8.3 Posterior Calculation	p. 150
8.4 Example: U.S. Cancer Mortality Atlas	p. 153
8.4.1 Breast Cancer	p. 154
8.4.2 Cervical Cancer	p. 155
8.4.3 Colorectal Cancer	p. 155
8.4.4 Lung Cancer	p. 159
8.4.5 Stomach Cancer	p. 159
8.5 Conclusions	p. 159
9 Analyzing Spatial Data Using Skew-Gaussian Processes	p. 163
9.1 Introduction	p. 163
9.2 Skew-Gaussian Processes	p. 164
9.2.1 The Model	p. 165
9.2.2 Bayesian Analysis	p. 166
9.2.3 Computational Strategy	p. 167
9.3 Real Data Illustration: Spatial Potential Data Prediction	p. 168
9.4 Discussion	p. 171
10 Accounting for Absorption Lines in Images Obtained with the Chandra X-ray Observatory	p. 175
10.1 Statistical Challenges of the Chandra X-ray Observatory	p. 175
10.2 Modeling the Image	p. 179
10.2.1 Model-Based Spatial Analysis	p. 179
10.2.2 Model-Based Spectral Analysis	p. 183
10.3 Absorption Lines	p. 184
10.3.1 Scientific Background	p. 184
10.3.2 Statistical Models	p. 185
10.3.3 Model Fitting	p. 188
10.3.4 A Simulation-Based Example	p. 190
10.4 Spectral Models with Absorption Lines	p. 192
10.4.1 Combining Models and Algorithms	p. 192
10.4.2 An Example	p. 195
10.5 Discussion	p. 196
11 Spatial Modelling of Count Data: A Case Study in Modelling Breeding Bird Survey Data on Large Spatial Domains	p. 199
11.1 Introduction	p. 199
11.2 The Poisson Random Effects Model	p. 200
11.2.1 Spectral Formulation	p. 202
11.2.2 Model Implementation and Prediction	p. 204
Selected Full-Conditional Distributions	p. 205
Prediction	p. 206
Implementation	p. 206
11.3 Results	p. 206
11.4 Conclusion	p. 207
III Spatio-temporal cluster modelling	p. 211
12 Modelling Strategies for Spatial-Temporal Data	p. 213
12.1 Introduction	p. 213
12.2 Modelling Strategy	p. 214
12.3 D-D (Drift-Drift) Models	p. 215
12.4 D-C (Drift-Correlation) Models	p. 220
12.5 C-C (Correlation-Correlation) Models	p. 222
12.6 A Unified Analysis on the Circle	p. 224
12.7 Discussion	p. 225
13 Spatio-Temporal Partition Modelling: An Example from Neurophysiology	p. 227
13.1 Introduction	p. 227
13.2 The Neurophysiological Experiment	p. 227
13.3 The Linear Inverse Solution	p. 228
13.4 The Mixture Model	p. 229
13.4.1 Initial Preparation of the Data	p. 229
13.4.2 Formulation of the Mixture Model	p. 230
13.5 Classification of the Inverse Solution	p. 232
13.6 Discussion	p. 234
14 Spatio-Temporal Cluster Modelling of Small Area Health Data	p. 235
14.1 Introduction	p. 235
14.2 Basic Cluster Modelling approaches	p. 235
14.2.1 Case Event Data Models	p. 236
Inter-Event versus Hidden Process Modelling	p. 236
14.2.2 Small Area Count Data Models	p. 239
14.2.3 Spatio-Temporal Extensions to Cluster Models	p. 239
14.3 A Spatio-Temporal Hidden Process Model	p. 240
14.4 Model Development	p. 240
14.4.1 Estimation of g(s,t)	p. 243
The Prior Distribution for Cluster Centres	p. 244
Choice of Cluster Distribution Function	p. 245
Other Prior Distributions and the Posterior Distribution	p. 245
14.4.2 Region Counts	p. 246
Integrated Intensity	p. 247
14.5 The Posterior Sampling Algorithm	p. 248
14.5.1 Goodness-of-Fit Measures for the Model	p. 249
14.6 Data Example: Scottish Birth Abnormalities	p. 249
14.6.1 Introduction	p. 249
14.6.2 Exploratory Analysis	p. 250
14.6.3 Model Fitting Results	p. 252
14.7 Discussion	p. 256
References	p. 259
Index	p. 277
Author Index	p. 281

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