Statistical Analysis and Modelling of Spatial Point PatternsISBN: 9780470014912
560 pages
February 2008

Description
Numerous aspects of the nature of a specific spatial point pattern may be described using the appropriate statistical methods. Statistical Analysis and Modelling of Spatial Point Patterns provides a practical guide to the use of these specialised methods. The applicationoriented approach helps demonstrate the benefits of this increasingly popular branch of statistics to a broad audience.
The book:
 Provides an introduction to spatial point patterns for researchers across numerous areas of application
 Adopts an extremely accessible style, allowing the nonstatistician complete understanding
 Describes the process of extracting knowledge from the data, emphasising the marked point process
 Demonstrates the analysis of complex datasets, using applied examples from areas including biology, forestry, and materials science
 Features a supplementary website containing example datasets.
Statistical Analysis and Modelling of Spatial Point Patterns is ideally suited for researchers in the many areas of application, including environmental statistics, ecology, physics, materials science, geostatistics, and biology. It is also suitable for students of statistics, mathematics, computer science, biology and geoinformatics.
Table of Contents
List of Examples.
1. Introduction.
1.1 Point process statistics.
1.2 Examples of point process data.
1.2.1 A pattern of amacrine cells.
1.2.2 Gold particles.
1.2.3 A pattern of Western Australian plants.
1.2.4 Waterstriders.
1.2.5 A sample of concrete.
1.3 Historical notes.
1.3.1 Determination of number of trees in a forest.
1.3.2 Number of blood particles in a sample.
1.3.3 Patterns of points in plant communities.
1.3.4 Formulating the power law for the pair correlation function for galaxies.
1.4 Sampling and data collection.
1.4.1 General remarks.
1.4.2 Choosing an appropriate study area.
1.4.3 Data collection.
1.5 Fundamentals of the theory of point processes.
1.6 Stationarity and isotropy.
1.6.1 Model approach and design approach.
1.6.2 Finite and infinite point processes.
1.6.3 Stationarity and isotropy.
1.6.4 Ergodicity.
1.7 Summary characteristics for point processes.
1.7.1 Numerical summary characteristics.
1.7.2 Functional summary characteristics.
1.8 Secondary structures of point processes.
1.8.1 Introduction.
1.8.2 Random sets.
1.8.3 Random fields.
1.8.4 Tessellations.
1.8.5 Neighbour networks or graphs.
1.9 Simulation of point processes.
2. The Homogeneous Poisson point process.
2.1 Introduction.
2.2 The binomial point process.
2.2.1 Introduction.
2.2.2 Basic properties.
2.2.3 The periodic binomial process.
2.2.4 Simulation of the binomial process.
2.3 The homogeneous Poisson point process.
2.3.1 Introduction.
2.3.2 Basic properties.
2.3.3 Characterisations of the homogeneous Poisson process.
2.4 Simulation of a homogeneous Poisson process.
2.5 Model characteristics.
2.5.1 Moments and moment measures.
2.5.2 The Palm distribution of a homogeneous Poisson process.
2.5.3 Summary characteristics of the homogeneous Poisson process.
2.6 Estimating the intensity.
2.7 Testing complete spatial randomness.
2.7.1 Introduction.
2.7.2 Quadrat counts.
2.7.3 Distance methods.
2.7.4 The Jtest.
2.7.5 Two indexbased tests.
2.7.6 Discrepancy tests.
2.7.7 The Ltest.
2.7.8 Other tests and recommendations.
3. Finite point processes.
3.1 Introduction.
3.2 Distributions of numbers of points.
3.2.1 The binomial distribution.
3.2.2 The Poisson distribution.
3.2.3 Compound distributions.
3.2.4 Generalised distributions.
3.3 Intensity functions and their estimation.
3.3.1 Parametric statistics for the intensity function.
3.3.2 Nonparametric estimation of the intensity function.
3.3.3 Estimating the point density distribution function.
3.4 Inhomogeneous Poisson process and finite Cox process.
3.4.1 The inhomogeneous Poisson process.
3.4.2 The finite Cox process.
3.5 Summary characteristics for finite point processes.
3.5.1 Nearestneighbour distances.
3.5.2 Dilation function.
3.5.3 Graphtheoretic statistics.
3.5.4 Secondorder characteristics.
3.6 Finite Gibbs processes.
3.6.1 Introduction.
3.6.2 Gibbs processes with fixed number of points.
3.6.3 Gibbs processes with a random number of points.
3.6.4 Secondorder summary characteristics of finite Gibbs processes.
3.6.5 Further discussion.
3.6.6 Statistical inference for finite Gibbs processes.
4. Stationary point processes.
4.1 Basic definitions and notation.
4.2 Summary characteristics for stationary point processes.
4.2.1 Introduction.
4.2.2 Edgecorrection methods.
4.2.3 The intensity λ.
4.2.4 Indices as summary characteristics.
4.2.5 Emptyspace statistics and other morphological summaries.
4.2.6 The nearestneighbour distance distribution function.
4.2.7 The Jfunction.
4.3 Secondorder characteristics.
4.3.1 The three functions: K, L and g.
4.3.2 Theoretical foundations of secondorder characteristics.
4.3.3 Estimators of the secondorder characteristics.
4.3.4 Interpretation of pair correlation functions.
4.4 Higherorder and topological characteristics.
4.4.1 Introduction.
4.4.2 Thirdorder characteristics.
4.4.3 Delaunay tessellation characteristics.
4.4.4 The connectivity function.
4.5 Orientation analysis for stationary point processes.
4.5.1 Introduction.
4.5.2 Nearestneighbour orientation distribution.
4.5.3 Secondorder orientation analysis.
4.6 Outliers, gaps and residuals.
4.6.1 Introduction.
4.6.2 Simple outlier detection.
4.6.3 Simple gap detection.
4.6.4 Modelbased outliers.
4.6.5 Residuals.
4.7 Replicated patterns.
4.7.1 Introduction.
4.7.2 Aggregation recipes.
4.8 Choosing appropriate observation windows.
4.8.1 General ideas.
4.8.2 Representative windows.
4.9 Multivariate analysis of series of point patterns.
4.10 Summary characteristics for the nonstationary case.
4.10.1 Formal application of stationary characteristics and estimators.
4.10.2 Intensity reweighting.
4.10.3 Local rescaling.
5. Stationary marked point processes.
5.1 Basic definitions and notation.
5.1.1 Introduction.
5.1.2 Marks and their properties.
5.1.3 Marking models.
5.1.4 Stationarity.
5.1.5 Firstorder characteristics.
5.1.6 Marksum measure.
5.1.7 Palm distribution.
5.2 Summary characteristics.
5.2.1 Introduction.
5.2.2 Intensity and marksum intensity.
5.2.3 Mean mark, mark d.f. and mark probabilities.
5.2.4 Indices for stationary marked point processes.
5.2.5 Nearestneighbour distributions.
5.3 Secondorder characteristics for marked point processes.
5.3.1 Introduction.
5.3.2 Definitions for qualitative marks.
5.3.3 Definitions for quantitative marks.
5.3.4 Estimation of secondorder characteristics.
5.4 Orientation analysis for marked point processes.
5.4.1 Introduction.
5.4.2 Orientation analysis for nonisotropic processes with angular marks.
5.4.3 Orientation analysis for isotropic processes with angular marks.
5.4.4 Orientation analysis with constructed marks.
6. Modelling and simulation of stationary point processes.
6.1 Introduction.
6.2 Operations with point processes.
6.2.1 Thinning.
6.2.2 Clustering.
6.2.3 Superposition.
6.3 Cluster processes.
6.3.1 General cluster processes.
6.3.2 NeymanScott processes.
6.4 Stationary Cox processes.
6.4.1 Introduction.
6.4.2 Properties of stationary Cox processes.
6.5 Hardcore point processes.
6.5.1 Introduction.
6.5.2 Matérn hardcore processes.
6.5.3 The dead leaves model.
6.5.4 The RSA model.
6.5.5 Random dense packings of hard spheres.
6.6 Stationary Gibbs processes.
6.6.1 Basic ideas and equations.
6.6.2 Simulation of stationary Gibbs processes.
6.6.3 Statistics for stationary Gibbs processes.
6.7 Reconstruction of point patterns.
6.7.1 Reconstructing point patterns without a specified model.
6.7.2 An example: reconstruction of NeymanScott processes.
6.7.3 Practical application of the reconstruction algorithm.
6.8 Formulas for marked point process models.
6.8.1 Introduction.
6.8.2 Independent marks.
6.8.3 Random field model.
6.8.4 Intensityweighted marks.
6.9 Moment formulas for stationary shotnoise fields.
6.10 Spacetime point processes.
6.10.1 Introduction.
6.10.2 Spacetime Poisson processes.
6.10.3 Secondorder statistics for completely stationary event processes.
6.10.4 Two examples of spacetime processes.
6.11 Correlations between point processes and other random structures.
6.11.1 Introduction.
6.11.2 Correlations between point processes and random fields.
6.11.3 Correlations between point processes and fibre processes.
7. Fitting and testing point process models.
7.1 Choice of model.
7.2 Parameter estimation.
7.2.1 Maximum likelihood method.
7.2.2 Method of moments.
7.2.3 Trialanderror estimation.
7.3 Variance estimation by bootstrap.
7.4 Goodnessoffit tests.
7.4.1 Envelope test.
7.4.2 Deviation test.
7.5 Testing mark hypotheses.
7.5.1 Introduction.
7.5.2 Testing independent marking, test of association.
7.5.3 Testing geostatistical marking.
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.
Author Information
Antti Pentinen, Professor in the Department of Mathematics and Statistics, University of Jyvaskyla, Finland
Dietrich Stoyan, Professor a the Insitut fur Stochastik, University of Freiberg, Germany
Reviews
"Statistical Analysis and Modelling of Spatial Point Patterns is an extremely wellwritten book and is accessible to a wide audience, including both applied statisticians and researchers from other fields with a reasonably sophisticated background in statics." (Journal of the American Statistical Association, September 2010)“The book presents statistical methods that are relevant in practice, focusing on traditional methods, in particular those based on summary statistics, but also more recent models and methods are briefly discussed. ”(Biometrics , September 2009)
"The book is a useful addition to Wiley's series Statistics in Practice." (Journal of Tropical Pediatrics, February 2009)
"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)
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