Statistical Analysis and Modelling of Spatial Point Patterns

Inhaltsverzeichnis

Preface.
 
List of Examples.
 
1. Introduction.
 
1.1 Point process statistics.
 
1.2 Examples of point process data.
 
1.3 Historical notes.
 
1.4 Sampling and data collection.
 
1.5 Fundamentals of the theory of point processes.
 
1.6 Stationarity and isotropy.
 
1.7 Summary characteristics for point processes.
 
1.8 Secondary structures of point processes.
 
1.9 Simulation of point processes.
 
2. The Homogeneous Poisson point process.
 
2.1 Introduction.
 
2.2 The binomial point process.
 
2.3 The homogeneous Poisson point process.
 
2.4 Simulation of a homogeneous Poisson process.
 
2.5 Model characteristics.
 
2.6 Estimating the intensity.
 
2.7 Testing complete spatial randomness.
 
3. Finite point processes.
 
3.1 Introduction.
 
3.2 Distributions of numbers of points.
 
3.3 Intensity functions and their estimation.
 
3.4 Inhomogeneous Poisson process and finite Cox process.
 
3.5 Summary characteristics for finite point processes.
 
3.6 Finite Gibbs processes.
 
4. Stationary point processes.
 
4.1 Basic definitions and notation.
 
4.2 Summary characteristics for stationary point processes.
 
4.3 Second-order characteristics.
 
4.4 Higher-order and topological characteristics.
 
4.5 Orientation analysis for stationary point processes.
 
4.6 Outliers, gaps and residuals.
 
4.7 Replicated patterns.
 
4.8 Choosing appropriate observation windows.
 
4.9 Multivariate analysis of series of point patterns.
 
4.10 Summary characteristics for the non-stationary case.
 
5. Stationary marked point processes.
 
5.1 Basic definitions and notation.
 
5.2 Summary characteristics.
 
5.3 Second-order characteristics for marked point processes.
 
5.4 Orientation analysis for marked point processes.
 
6. Modelling and simulation of stationary point processes.
 
6.1 Introduction.
 
6.2 Operations with point processes.
 
6.3 Cluster processes.
 
6.4 Stationary Cox processes.
 
6.5 Hard-core point processes.
 
6.6 Stationary Gibbs processes.
 
6.7 Reconstruction of point patterns.
 
6.8 Formulas for marked point process models.
 
6.9 Moment formulas for stationary shot-noise fields.
 
6.10 Space-time point processes.
 
6.11 Correlations between point processes and other random structures.
 
7. Fitting and testing point process models.
 
7.1 Choice of model.
 
7.2 Parameter estimation.
 
7.3 Variance estimation by bootstrap.
 
7.4 Goodness-of-fit tests.
 
7.5 Testing mark hypotheses.
 
7.6 Bayesian methods for point pattern analysis.
 
Appendix A Fundamentals of statistics.
 
Appendix B Geometrical characteristics of sets.
 
Appendix C Fundamentals of geostatistics.
 
References.
 
Notation index.
 
Author index.
 
Subject index.

Statistical Analysis and Modelling of Spatial Point Patterns

From Spatial Data to Knowledge

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Rezension

"The abstract flavor this brings to the subject means that methods may have very wide applicability over different application domains. This applicability, in turn, is reflected by the large number of interesting examples described in the book. The book provides a comprehensive overview of the area." International Statistical Review ( December 2008)

Details

Einband

Gebundene Ausgabe

Erscheinungsdatum

01.03.2008

Verlag

John Wiley & Sons Inc

Seitenzahl

544

Maße (L/B/H)

23,5/15,7/3,4 cm

Rezension

Details

Einband

Gebundene Ausgabe

Erscheinungsdatum

01.03.2008

Verlag

John Wiley & Sons Inc

Seitenzahl

544

Maße (L/B/H)

23,5/15,7/3,4 cm

Gewicht

954 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-0-470-01491-2

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  • Statistical Analysis and Modelling of Spatial Point Patterns
  • Preface.
     
    List of Examples.
     
    1. Introduction.
     
    1.1 Point process statistics.
     
    1.2 Examples of point process data.
     
    1.3 Historical notes.
     
    1.4 Sampling and data collection.
     
    1.5 Fundamentals of the theory of point processes.
     
    1.6 Stationarity and isotropy.
     
    1.7 Summary characteristics for point processes.
     
    1.8 Secondary structures of point processes.
     
    1.9 Simulation of point processes.
     
    2. The Homogeneous Poisson point process.
     
    2.1 Introduction.
     
    2.2 The binomial point process.
     
    2.3 The homogeneous Poisson point process.
     
    2.4 Simulation of a homogeneous Poisson process.
     
    2.5 Model characteristics.
     
    2.6 Estimating the intensity.
     
    2.7 Testing complete spatial randomness.
     
    3. Finite point processes.
     
    3.1 Introduction.
     
    3.2 Distributions of numbers of points.
     
    3.3 Intensity functions and their estimation.
     
    3.4 Inhomogeneous Poisson process and finite Cox process.
     
    3.5 Summary characteristics for finite point processes.
     
    3.6 Finite Gibbs processes.
     
    4. Stationary point processes.
     
    4.1 Basic definitions and notation.
     
    4.2 Summary characteristics for stationary point processes.
     
    4.3 Second-order characteristics.
     
    4.4 Higher-order and topological characteristics.
     
    4.5 Orientation analysis for stationary point processes.
     
    4.6 Outliers, gaps and residuals.
     
    4.7 Replicated patterns.
     
    4.8 Choosing appropriate observation windows.
     
    4.9 Multivariate analysis of series of point patterns.
     
    4.10 Summary characteristics for the non-stationary case.
     
    5. Stationary marked point processes.
     
    5.1 Basic definitions and notation.
     
    5.2 Summary characteristics.
     
    5.3 Second-order characteristics for marked point processes.
     
    5.4 Orientation analysis for marked point processes.
     
    6. Modelling and simulation of stationary point processes.
     
    6.1 Introduction.
     
    6.2 Operations with point processes.
     
    6.3 Cluster processes.
     
    6.4 Stationary Cox processes.
     
    6.5 Hard-core point processes.
     
    6.6 Stationary Gibbs processes.
     
    6.7 Reconstruction of point patterns.
     
    6.8 Formulas for marked point process models.
     
    6.9 Moment formulas for stationary shot-noise fields.
     
    6.10 Space-time point processes.
     
    6.11 Correlations between point processes and other random structures.
     
    7. Fitting and testing point process models.
     
    7.1 Choice of model.
     
    7.2 Parameter estimation.
     
    7.3 Variance estimation by bootstrap.
     
    7.4 Goodness-of-fit tests.
     
    7.5 Testing mark hypotheses.
     
    7.6 Bayesian methods for point pattern analysis.
     
    Appendix A Fundamentals of statistics.
     
    Appendix B Geometrical characteristics of sets.
     
    Appendix C Fundamentals of geostatistics.
     
    References.
     
    Notation index.
     
    Author index.
     
    Subject index.