Janine Illian, Antti Penttinen, Helga Stoyan, Dietrich Stoyan

Statistical Analysis and Modelling of Spatial Point Patterns (eBook, PDF)

• Format: PDF

Produktbeschreibung

Spatial point processes are mathematical models used to describe and analyse the geometrical structure of patterns formed by objects that are irregularly or randomly distributed in one-, two- or three-dimensional space. Examples include locations of trees in a forest, blood particles on a glass plate, galaxies in the universe, and particle centres in samples of material. 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 application-oriented 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 non-statistician 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.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 560
• Erscheinungstermin: 2. August 2008
• Englisch
• ISBN-13: 9780470725153
• Artikelnr.: 37299064

Autorenporträt

Janine Illian, SIMBIOS, University of Abertay, Dundee, Scotland. Antti Pentinen, Professor in the Department of Mathematics and Statistics, University of Jyvaskyla, Finland. Dietrich Stoyan, Professor a the Insitut für Stochastik, University of Freiberg, Germany.

Inhaltsangabe

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.