Statistical Analysis of Spatial Point Patterns

by Diggle, Peter J.

• ISBN13: 9780340740705
• ISBN10: 0340740701
• Edition: 2nd
• Format: Hardcover
• Copyright: 2003-03-20
• Publisher: Hodder Education Publishers

Summary

This is a new edition of the classic monograph, published in 1983, that described those statistical methods that are used to analyse spatial data. This edition has been entirely updated with the latest developments in the analysis of spatial data which have grown to become a large area ofconcern in environmental and epidemiological research. There is a website connected with the volume that contains additional data sets and a new chapter on spatial epidemiology. It is appropriate for graduate level statisticians in various disciplines.

Author Biography

Peter J Diggle is Professor of Statistics at Lancaster University, UK

Table of Contents

Preface	vii
Introduction	1	(11)
Spatial point patterns	1	(2)
Sampling	3	(2)
Edge effects	5	(1)
Complete spatial randomness	6	(1)
Objectives of statistical analysis	7	(1)
The Dirichlet tessellation	8	(1)
Monte Carlo tests	9	(1)
Software	10	(2)
Preliminary testing	12	(18)
Tests of complete spatial randomness	12	(1)
Inter-event distances	13	(4)
Analysis of Japanese black pine saplings	14	(1)
Analysis of redwood seedlings	14	(2)
Analysis of biological cells	16	(1)
Small distances	16	(1)
Nearest neighbour distances	17	(4)
Analysis of Japanese black pine saplings	19	(1)
Analysis of redwood seedlings	19	(1)
Analysis of biological cells	19	(2)
Point-to-nearest-event distances	21	(2)
Analysis of Japanese black pine saplings	22	(1)
Analysis of redwood seedlings	22	(1)
Analysis of biological cells	22	(1)
Quadrat counts	23	(2)
Analysis of Japanese black pine saplings	24	(1)
Analysis of redwood seedlings	24	(1)
Analysis of biological cells	25	(1)
Scales of pattern	25	(3)
Analysis of Lansing Woods data	26	(1)
Scales of dependence	27	(1)
Recommendations	28	(2)
Statistical methods for sparsely sampled patterns	30	(12)
General remarks	30	(1)
Quadrat counts	31	(2)
Tests of CSR	31	(1)
Estimators of intensity	32	(1)
Analysis of Lansing Woods data	32	(1)
Distance methods	33	(7)
Distribution theory under CSR	33	(2)
Tests of CSR	35	(4)
Estimators of intensity	39	(1)
Analysis of Lansing Woods data	40	(1)
Tests of independence	40	(1)
Recommendations	41	(1)
Spatial point processes	42	(21)
Processes and summary descriptions	42	(1)
Second-order properties	43	(3)
Univariate processes	43	(2)
Extension to multivariate processes	45	(1)
Higher-order moments and nearest neighbour distributions	46	(1)
The homogeneous Poisson process	47	(1)
Independence and random labelling	48	(1)
Estimation of second-order properties	49	(9)
Univariate processes	49	(6)
Inhomogeneous processes	55	(1)
Multivariate processes	55	(1)
Examples	56	(2)
Displaced amacrine cells in the retina of a rabbit	58	(2)
Estimation of nearest neighbour distributions	60	(2)
Examples	61	(1)
Concluding remarks	62	(1)
Models	63	(23)
Introduction	63	(1)
Contagious distributions	63	(1)
Poisson cluster processes	64	(3)
Inhomogeneous Poisson processes	67	(1)
Cox processes	68	(4)
Simple inhibition processes	72	(2)
Markov point processes	74	(4)
Pairwise interaction point processes	75	(3)
More general forms of interaction	78	(1)
Other constructions	78	(4)
Lattice-based processes	78	(1)
Thinned processes	79	(1)
Superpositions	80	(1)
Interactions in an inhomogeneous environment	81	(1)
Multivariate models	82	(4)
Marked point processes	82	(1)
Multivariate point processes	82	(1)
How should multivariate models be formulated?	82	(1)
Cox processes	83	(2)
Markov point processes	85	(1)
Model-fitting using summary descriptions	86	(18)
Parameter estimation using the K-function	86	(3)
Least squares estimation	86	(1)
Illustration for simulations of a Poisson cluster process	87	(1)
Procedure when K (t) is unknown	88	(1)
Goodness-of-fit assessment using nearest neighbour distributions	89	(1)
Examples	90	(10)
Redwood seedlings	90	(2)
Bramble canes	92	(8)
Parameter estimation via goodness-of-fit testing	100	(4)
Analysis of hamster tumour data	100	(4)
Model-fitting using likelihood-based methods	104	(11)
Likelihood inference for inhomogeneous Poisson processes	104	(3)
Fitting a trend surface to the Lansing Woods data	105	(2)
Likelihood inference for Markov point processes	107	(7)
Maximum pseudo-likelihood estimation	107	(2)
Non-parametric estimation of a pairwise interaction function	109	(1)
Fitting a pairwise interaction point process to the displaced amacrine cells	109	(1)
Monte Carlo maximum likelihood estimation	110	(3)
The displaced amacrine cells revisited	113	(1)
Further reading	114	(1)
Non-parametric methods	115	(13)
Estimating weighted integrals of the second-order intensity	115	(1)
Non-parametric estimation of a spatially varying intensities	116	(5)
Estimating spatially varying intensity for the Lansing Woods data	118	(3)
Analysing replicated spatial point patterns	121	(7)
Estimating the K-function from replicated data	123	(1)
Between-group comparisons in designed experiments	124	(3)
Parametric or non-parametric methods?	127	(1)
Point process methods in spatial epidemiology	128	(17)
Introduction	128	(2)
Spatial clustering	130	(3)
Analysis of the North Humberside childhood leukaemia data	131	(1)
Other tests of spatial clustering	132	(1)
Spatial variation in risk	133	(1)
Point source models	134	(5)
Childhood asthma in North Derbyshire, England	137	(1)
Cancers in North Liverpool	137	(2)
Stratification and matching	139	(4)
Stratified case-control designs	139	(2)
Individually matched case-control designs	141	(2)
Is stratification or matching helpful?	143	(1)
Disentangling heterogeneity and clustering	143	(2)
References	145	(10)
Index	155