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9780387283111

Case Studies in Spatial Point Process Modeling

by ; ; ; ;
  • ISBN13:

    9780387283111

  • ISBN10:

    0387283110

  • Format: Paperback
  • Copyright: 2006-01-01
  • Publisher: Springer Nature
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Summary

Point process statistics is successfully used in fields such as material science, human epidemiology, social sciences, animal epidemiology, biology, and seismology. Its further application depends greatly on good software and instructive case studies that show the way to successful work. This book satisfies this need by a presentation of the spatstat package and many statistical examples. Researchers, spatial statisticians and scientists from biology, geosciences, materials sciences and other fields will use this book as a helpful guide to the application of point process statistics. No other book presents so many well-founded point process case studies.

Table of Contents

Preface v
List of Contributors xv
Part I Basic Notions and Manipulation of Spatial Point Processes
Fundamentals of Point Process Statistics
Dietrich Stoyan
3(20)
1 Basic Notions of the Theory of Spatial Point Processes
3(2)
2 Marked Point Processes
5(1)
3 The Second-order Moment Measure
6(3)
4 Introduction to Statistics for Planar Point Processes
9(8)
5 The Homogeneous Poisson Point Process
17(3)
6 Other Point Processes Models
20(1)
References
21(2)
Modelling Spatial Point Patterns in R
Adrian Baddeley, Rolf Turner
23(54)
1 Introduction
23(1)
2 The spatstat Package
23(1)
2.1 Scope
24(1)
2.2 Data Types in spatstat
24(1)
3 Data Analysis in spatstat
25(1)
3.1 Data Input
25(1)
3.2 Initial Inspection of Data
26(1)
3.3 Exploratory Data Analysis
27(1)
4 Point Process Models
27(1)
4.1 Formulation of Models
28(1)
4.2 Scope of Models
29(1)
4.3 Model-fitting Algorithm
29(1)
5 Model-fitting in spatstat
30(1)
5.1 Overview
30(1)
5.2 Spatial Trend Terms
31(1)
5.3 Interaction Terms
32(1)
6 Fitted Models
33(1)
6.1 Interpretation of Fitted Coefficients
34(1)
6.2 Invalid Models
35(1)
6.3 Predicting and Plotting a Fitted Model
36(1)
7 Models with Covariates
37(1)
7.1 Covariates in a List of Images
38(1)
7.2 Covariates in a Data Frame
40(1)
8 Fitting Models to Multitype Point Patterns
41(1)
8.1 Conditional Intensity
41(1)
8.2 Multitype Models
42(2)
9 Irregular Parameters
44(1)
10 Model Validation
45(1)
10.1 Residuals and Diagnostics
46(1)
10.2 Formal Inference
46(4)
11 Harkness-Isham Ants' Nests Data
50(1)
11.1 Description of Data
50(1)
11.2 Exploratory Analysis
51(3)
11.3 Modelling
54(3)
11.4 Formal Inference
57(2)
11.5 Incorporation of Covariates
59(3)
12 The Queensland Copper Data
62(1)
12.1 Data and Previous Analyses
62(1)
12.2 Analysis
63(6)
12.3 North-South Effect
69(1)
References
70(7)
Part II Theoretical and Methodological Advances in Spatial Point Processes
Strong Markov Property of Poisson Processes and Slivnyak Formula
Sergei Zuyev
77(8)
1 Filtrations and Stopping Sets
77(4)
2 Slivnyak Theorem for Locally Defined Processes
81(3)
References
84(1)
Bayesian Analysis of Markov Point Processes
Kasper K. Berthelsen, Asper Møller
85(14)
1 Introduction
85(3)
2 Auxiliary Variable Method
88(1)
3 The Strauss Process
89(1)
3.1 Specification of Auxiliary Point Processes
89(2)
3.2 Results for the Auxiliary Variable Method
91(2)
4 Concluding Remarks
93(3)
References
96(3)
Statistics for Locally Scaled Point Processes
Michaela Prokešová, Ute Hahn, Eva B. Vedel Jensen
99(26)
1 Introduction
99(2)
2 Locally Scaled Point Processes
101(3)
3 Simultaneous Maximum (Pseudo)likelihood Estimation of Scaling Function and Template Parameters
104(2)
4 Two Step Maximum Likelihood Estimation of Scaling Parameters Prior to Template Parameters
106(1)
4.1 Estimation of Scaling Parameters, Using the Poisson Likelihood
107(2)
4.2 Statistical Properties of theta0
109(1)
4.3 Estimation of the Template Parameters
110(1)
5 Simulation Study
111(3)
6 Two Step Inference Where Scaling Function Is Estimated Using Other (non ML) Methods
114(1)
7 Model Validation
115(1)
7.1 The K-function
116(1)
7.2 The Q² Statistic
117(1)
8 Data Analysis
118(4)
References
122(3)
Nonparametric Testing of Distribution Functions in Germ-grain Models
Zbynek Pawlas, Lothar Heinrich
125(10)
1 Introduction
125(2)
2 Empirical Distribution Functions
127(1)
3 Weak Convergence of an Empirical Multiparameter Process
128(1)
4 Centres of Pores in a Ceramic Coating
129(3)
5 Conclusion
132(1)
References
133(2)
Principal Component Analysis for Spatial Point Processes – Assessing the Appropriateness of the Approach in an Ecological Context
Janine Illian, Erica Benson, John Crawford, Harry Staines
135(18)
1 Introduction
135(1)
2 Methods
136(1)
2.1 Functional Data Analysis
136(1)
2.2 Functional Principal Component Analysis of Second-Order Summary Statistics
137(1)
3 Feasibility Study
138(2)
4 Erroneous Data
140(2)
4.1 Inaccurate Location
142(1)
4.2 Data Collected on a Grid
142(2)
4.3 Wrong Species Recorded
144(2)
5 Application
146(2)
6 Discussion
148(1)
References
149(4)
Part III Practical Applications of Spatial Point Processes
On Modelling of Refractory Castables by Marked Gibbs and Gibbsian-like Processes
Felix Ballani
153(16)
1 Introduction
153(1)
2 The Data
154(1)
2.1 Production and Data Extraction
155(1)
2.2 Statistics
155(2)
3 The Stationary Marked Gibbs Process
157(2)
4 The Random-Shift Model
159(1)
4.1 Definition
159(1)
4.2 Simulation
160(2)
4.3 Fitting
162(2)
5 Further Models
164(1)
5.1 Dense Random Packings
164(1)
5.2 The Ordered RSA Model
164(1)
6 Conclusions
165(1)
References
165(4)
Source Detection in an Outbreak of Legionnaire's Disease
Miguel A. Martinez-Beneito, Juan J. Abellán, Antonio López-Quliez, Hermelinda Vanaclocha, Óscar Zurriaga, Guillermo Jorques, José Fenollor
169(14)
1 Introduction
169(1)
2 Case Study Description
170(2)
3 Methods
172(4)
4 Results
176(1)
5 Discussion
177(4)
References
181(2)
Doctors' Prescribing Patterns in the Midi-Pyrenees rRegion of France: Point-process Aggregation
Noel A.C. Cressie, Olivier Perrin, Christine Thomas-Agnan
183(14)
1 Introduction
183(2)
2 Spatial Regression Model
185(3)
3 Weighted Regression Analysis
188(3)
4 Weighted Spatial Regression Analysis
191(3)
5 Discussion and conclusions
194(1)
References
195(2)
Strain-typing Transmissible Spongiform Encephalopathies Using Replicated Spatial Data
Simon Webster, Peter J. Diggle, Helen E. Clough, Robert B. Green, Nigel P. French
197(18)
1 Introduction
197(2)
2 Data Collection
199(1)
2.1 Sample Material
199(2)
2.2 Extraction of Data from the Sample Material
201(1)
3 Methods
202(1)
3.1 Vacuole Counts
202(1)
3.2 Vacuole Sizes
203(1)
3.3 Spatial Distribution
203(3)
4 Results
206(1)
4.1 Vacuole Counts
206(2)
4.2 Vacuole Sizes
208(2)
4.3 Spatial Distribution of Vacuoles
210(2)
5 Discussion
212(1)
References
213(2)
Modelling the Bivariate Spatial Distribution of Amacrine Cells
Peter J. Diggle, Stephen J. Eglen, John B. Troy
215(20)
1 Introduction
215(1)
1.1 Biological Background
215(3)
2 Pairwise Interaction Point Processes
218(1)
2.1 Univariate Pairwise Interaction Point Processes
218(3)
2.2 Bivariate Pairwise Interaction Point Processes
221(1)
3 Monte Carlo Likelihood Inference
222(1)
4 Analysis of the Amacrines Data
223(1)
4.1 Exploratory Analysis
223(2)
4.2 Structural Hypotheses for the Amacrines Data
225(1)
4.3 Non-parametric Estimation
225(1)
4.4 Univariate Parametric Analysis
226(2)
4.5 Bivariate Analysis
228(2)
5 Conclusions
230(1)
5.1 Statistical Summary
230(1)
5.2 Biological Implications
230(2)
References
232(3)
Analysis of Spatial Point Patterns in Microscopic and Macroscopic Biological Image Data
Frank Fleischer, Michael Beil, Marian Kazda, Volker Schmidt
235(26)
1 Introduction
235(1)
1.1 Analysis of Centromeric Heterochromatin Structures
236(1)
1.2 Planar Sections of Root Systems in Tree Stands
237(1)
1.3 Detection of Structural Differences
238(1)
2 Image Data
238(1)
2.1 NB4 Cell Nuclei
238(1)
2.2 Profile Walls
239(2)
3 Statistical Methods and Results
241(1)
3.1 3D Point Patterns of Chromocenters in NB4 Cells
241(3)
3.2 2D Point Patterns in Planar Sections of Root Systems
244(3)
3.3 Model Fitting for the Root Data
247(3)
4 Discussion
250(1)
4.1 NB4 Cell Nuclei
250(2)
4.2 Planar Sections of Root Systems
252(5)
References
257(4)
Spatial Marked Point Patterns for Herd Dispersion in a Savanna Wildlife Herbivore Community in Kenya
Alfred Stein, Nick Georgiadis
261(14)
1 Introduction
261(1)
2 Materials and Methods
262(1)
2.1 Distribution Data
262(2)
2.2 Measures of Dispersion
264(2)
3 Results
266(1)
3.1 Spatial Point Patterns
266(3)
4 Discussion
269(2)
5 Conclusions
271(1)
References
272(3)
Diagnostic Analysis of Space-Time Branching Processes for Earthquakes
Jiancang Zhaang, Yosihiko Ogata, David Vere-Jones
275(18)
1 Introduction
275(1)
2 The Space-time ETAS Model
276(4)
3 Data and Preliminary Results
280(2)
4 Residual Analysis for the Whole Process
282(2)
5 Verifying Stationarity of the Background
284(2)
6 Verifying Formulation of Branching Structures by Stochastic Reconstruction
286(3)
7 Conclusion
289(1)
References
290(3)
Assessing Spatial Point Process Models Using Weighted K-functions: Analysis of California Earthquakes
Alejandro Veen, Frederic Paik Schoenberg
293
1 Introduction
293(1)
2 The Weighted K-function
294(1)
2.1 Ripley's K-function and Variants
294(1)
2.2 Definition and Distribution of the Weighted K-function
295(3)
3 Application
298(1)
3.1 Data Set
298(1)
3.2 Analysis
299(4)
4 Concluding Remarks
303(1)
References
304

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