Statistical Analysis of Spatial and Spatio-Temporal Point Patterns

ISBN-10: 1466560231
ISBN-13: 9781466560239
Edition: 3rd 2013 (Revised)
Authors: Peter J. Diggle
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Description: The first edition of this perennial bestseller broke new ground in the then emerging subject of spatial statistics with its coverage of the statistical analysis of spatial point patterns. Completely revised and updated, the third edition includes  More...

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Book details

Edition: 3rd
Copyright year: 2013
Publisher: Taylor & Francis Group
Publication date: 7/23/2013
Binding: Hardcover
Pages: 268
Size: 6.25" wide x 9.25" long x 1.00" tall
Weight: 1.782
Language: English

The first edition of this perennial bestseller broke new ground in the then emerging subject of spatial statistics with its coverage of the statistical analysis of spatial point patterns. Completely revised and updated, the third edition includes discussion of spatio-temporal point patterns, covering the acceleration of methodological development and diversification of application. Reflecting another major development since the publication of the second edition, this edition includes R code and makes the data sets and R code used in the book available on the book’s web page.

List of Figures
List of Tables
Preface
Introduction
Spatial point patterns
Sampling
Edge-effects
Complete spatial randomness
Objectives of statistical analysis
The Dirichlet tessellation
Monte Carlo tests
Software
Preliminary testing
Tests of complete spatial randomness
Inter-event distances
Analysis of Japanese black pine saplings
Analysis of redwood seedlings
Analysis of biological cells
Small distances
Nearest neighbour distances
Analysis of Japanese black pine saplings
Analysis of redwood seedlings
Analysis of biological cells
Point to nearest event distances
Analysis of Japanese black pine seedlings
Analysis of redwood seedlings
Analysis of biological cells
Quadrat counts
Analysis of Japanese black pine seedlings
Analysis of redwood seedlings
Analysis of biological cells
Scales of pattern
Analysis of Lansing Woods data
Scales of dependence
Recommendations
Methods for sparsely sampled patterns
General remarks
Quadrat counts
Tests of CSR
Estimators of intensity
Analysis of Lansing Woods data
Distance measurements
Distribution theory under CSR
Tests of CSR
Estimators of intensity
Analysis of Lansing Woods data
Catana's wandering quarter
Tests of independence
Recommendations
Spatial point processes
Processes and summary description's
Second-order properties
Univariate processes
Extension to multivariate processes
Higher order moments and nearest neighbour distributions
The homogeneous Poisson process
Independence and random labelling
Estimation of second-order properties
Stationary processes
Estimating the pair correlation function
Intensity-reweighted stationary processes
Multivariate processes
Examples
Displaced amacrine cells in the retina of a rabbit
Estimation of nearest neighbour distributions
Examples
Concluding remarks
Nonparametric methods
Introduction
Estimating weighted integrals of the second-order intensity
Nonparametric estimation of a spatially varying intensity
Estimating spatially varying intensities for the Lansing Woods data
Analysing replicated spatial point patterns
Estimating the K-function from replicated data
Between-group comparisons in designed experiments
Parametric or nonparametric methods?
Models
Introduction
Contagious distributions
Poisson cluster processes
Inhomogeneous Poisson processes
Cox processes
Trans-Gaussian Cox processes
Simple inhibition processes
Markov point processes
Pairwise interaction point processes
More general forms of interaction
Other constructions
Lattice-based processes
Thinned processes
Superpositions
Interactions in an inhomogeneous environment
Multivariate models
Marked point processes
Multivariate point processes
How should multivariate models be formulated?
Cox processes
Markov point processes
Model-fitting using summary descriptions
Introduction
Parameter estimation using the K-function
Least squares estimation
Simulated realisations of a Poisson cluster process
Procedure when K(t) is unknown
Goodness-of-fit assessment using nearest neighbour distributions
Examples
Redwood seedlings
Bramble canes
Parameter estimation via goodness-of-fit testing
Analysis of hamster tumour data
Model-fitting using likelihood-based methods
Introduction
Likelihood inference for inhomogeneous Poisson processes
Fitting a trend surface to the Lansing Woods data
Likelihood inference for Markov point processes
Maximum pseudo-likelihood estimation
Non-parametric estimation of a pairwise interaction function
Fitting a pairwise interaction point process to the displaced amacrine cells
Monte Carlo maximum likelihood estimation
The displaced amacrine cells re-visited
A bivariate model for the displaced amacrine cells
Likelihood inference for Cox processes
Predictive inference in a log-Gaussian Cox process
Non-parametric estimation of an intensity surface: hickories in Lansing Woods
Additional reading
Point process methods in spatial epidemiology
Introduction
Spatial clustering
Analysis of the North Humberside childhood leukaemia data
Other tests of spatial clustering
Spatial variation in risk
Primary biliary cirrhosis in the North East of England
Point source models
Childhood asthma in north Derbyshire, England
Cancers in North Liverpool
Stratification and matching
Stratified case-control designs
Individually matched case-control designs
Is stratification or matching helpful?
Disentangling heterogeneity and clustering
Spatio-temporal point processes
Introduction
Motivating examples
Gastro-intestinal illness in Hampshire, UK
The 2001 foot-and-mouth epidemic in Cumbria, UK
Bovine tuberculosis in Cornwall, UK
A classification of spatio-temporal point patterns and processes
Second-order properties
Conditioning on the past
Empirical and mechanistic models
Exploratory analysis
Introduction
Animation
Marginal and conditional summaries
Bovine tuberculosis in Cornwall, UK
Second-order properties
Stationary processes
Intensity-reweighted stationary processes
Campylobacteriosis in Lancashire, UK
Empirical models and methods
Introduction
Poisson processes
Cox processes
Separable and non-separable models
Log-Gaussian Cox processes
Inference
Gastro-intestinal illness in Hampshire, UK
Concluding remarks: point processes and geostatistics
Mechanistic models and methods
Introduction
Conditional intensity and likelihood
Partial likelihood
The 2001 foot-and-mouth epidemic in Cumbria, UK
Nesting patterns of Arctic terns
References
Index

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