| |
| |
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 | |