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Residual analysis for spatial point processes (with discussion
 Journal of the Royal Statistical Society (series B
, 2005
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[Read before The Royal Statistical Society at a meeting organized by the Research Section on
An estimating function approach to inference for inhomogeneous NeymanScott processes
 Biometrics
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Modelling spatial point patterns in R
 Case Studies in Spatial Point Pattern Modelling. Lecture Notes in Statistics 185, 23–74
, 2006
"... Summary. We describe practical techniques for fitting stochastic models to spatial point pattern data in the statistical package R. The techniques have been implemented in our package spatstat in R. They are demonstrated on two example datasets. 1 ..."
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Summary. We describe practical techniques for fitting stochastic models to spatial point pattern data in the statistical package R. The techniques have been implemented in our package spatstat in R. They are demonstrated on two example datasets. 1
Modern statistics for spatial point processes
, 2006
"... We summarize and discuss the current state of spatial point process theory and directions for future research, making an analogy with generalized linear models and random effect models, and illustrating the theory with various examples of applications. In particular, we consider Poisson, Gibbs, and ..."
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We summarize and discuss the current state of spatial point process theory and directions for future research, making an analogy with generalized linear models and random effect models, and illustrating the theory with various examples of applications. In particular, we consider Poisson, Gibbs, and Cox process models, diagnostic tools and model checking, Markov chain Monte Carlo algorithms, computational methods for likelihoodbased inference, and quick nonlikelihood approaches to inference.
Twostep estimation for inhomogeneous spatial point processes
 In preparation
, 2007
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Simulationbased Inference for Spatial Point Processes
, 2001
"... Introduction Spatial point processes play a fundamental role in spatial statistics. In the simplest case they model \small" objects that may be identied by a map of points showing stores, towns, plants, nests, galaxies or cases of a disease observed in a two or three dimensional region. The po ..."
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Cited by 13 (1 self)
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Introduction Spatial point processes play a fundamental role in spatial statistics. In the simplest case they model \small" objects that may be identied by a map of points showing stores, towns, plants, nests, galaxies or cases of a disease observed in a two or three dimensional region. The points may be decorated with marks (such as sizes or types) whereby marked point processes are obtained. The areas of applications are manifold: astronomy, geography, ecology, forestry, spatial epidemiology, image analysis, and many more. Currently spatial point processes is an active area of research, which probably will be of increasing importance for many new applications, as new technology such as geographical information systems makes huge amounts of spatial point process data available. Textbooks and review articles on dierent aspects of spatial point processes include Matheron (1975), Ripley (1977), Ripley (1981), Diggle (1983), Penttinen (1984), Daley &VereJones (1988),
A toolbox for fitting complex spatial point process models using integrated Laplace transformation (INLA)
, 2010
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Principal component analysis for spatial point processes  assessing the appropriateness of the approach in an ecological context
 Lecture Notes in Statistics, 185:135–150
, 2006
"... Spatial point processes are complex stochastic models. Their complexity increases with the number of types in a multitype point pattern due to the increasing number of potential interand intratype interactions and thus the increasing number of parameters complicating simulation and estimation. Th ..."
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Cited by 8 (1 self)
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Spatial point processes are complex stochastic models. Their complexity increases with the number of types in a multitype point pattern due to the increasing number of potential interand intratype interactions and thus the increasing number of parameters complicating simulation and estimation. This calls for a statistical method which reduces the dimensionality of the
Testing Separability in SpatialTemporal Marked Point Processes
, 2004
"... Summary. Nonparametric tests for investigating the separability of a spatialtemporal marked point process are described and compared. It is shown that a Cramer–von Misestype test is very powerful at detecting gradual departures from separability, and that a residual test based on randomly rescalin ..."
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Summary. Nonparametric tests for investigating the separability of a spatialtemporal marked point process are described and compared. It is shown that a Cramer–von Misestype test is very powerful at detecting gradual departures from separability, and that a residual test based on randomly rescaling the process is powerful at detecting nonseparable clustering or inhibition of the marks. An application to Los Angeles County wildfire data is given, in which it is shown that the separability hypothesis is invalidated largely due to clustering of fires of similar sizes within periods of up to 3.9 years.
Nonparametric Measures of Association between a Spatial Point Process and a Random Set
"... In mining exploration it is often desired to predict the occurrence of ore deposits given other geological information, such as the locations of faults. More generally it is of interest to measure the spatial association between two spatial patterns observed in the same survey region. Berman (198 ..."
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In mining exploration it is often desired to predict the occurrence of ore deposits given other geological information, such as the locations of faults. More generally it is of interest to measure the spatial association between two spatial patterns observed in the same survey region. Berman (1986) developed parametric methods for conditional inference about a point process X given another spatial process Y . This paper proposes an alternative, nonparametric approach using distance methods, analogous to the use of the summary functions F , G and J for univariate point patterns. Our methods apply to a bivariate spatial process (X; Y ) consisting of a point process X and a random set Y . In particular we develop a bivariate analogue of the Jfunction of Van Lieshout and Baddeley (1997), which shows promise as a summary statistic, and turns out to be closely related to Berman's analysis. Properties of the bivariate Jfunction include a multiplicative identity under independent superposition, which has no analogue in the univariate case. Two geological examples are investigated. Keywords: empty space function, first contact distribution, geological lineaments, goodnessof fit testing, Jfunction, line segment process, marked point process, Monte Carlo tests, Address for correspondence: Department of Mathematics & Statistics, University of Western Australia, Nedlands WA 6907, Australia. adrian@maths.uwa.edu.au ore deposits, Palm distribution, point processes, random sets, spatial statistics. AMS Mathematics Subject Classification (1995 Revision): Primary: 60D05. Secondary: 60G55, 62M30, 62G05. 2 1