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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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An estimating function approach to inference for inhomogeneous NeymanScott processes
 Biometrics
"... processes ..."
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
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 points ..."
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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),
Twostep estimation for inhomogeneous spatial point processes
 In preparation
, 2007
"... processes ..."
Likelihoodbased inference for clustered line transect data
 J. Agric. Biol. Environ. Stat
, 2006
"... data ..."
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
Nonparametric Bayesian inference for inhomogeneous Markov point processes
, 2006
"... With reference to a specific data set, we consider how to perform a flexible nonparametric Bayesian analysis of an inhomogeneous point pattern modelled by a Markov point process, with a location dependent first order term and pairwise interaction only. A priori we assume that the first order term i ..."
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With reference to a specific data set, we consider how to perform a flexible nonparametric Bayesian analysis of an inhomogeneous point pattern modelled by a Markov point process, with a location dependent first order term and pairwise interaction only. A priori we assume that the first order term is a shot noise process, and the interaction function for a pair of points depends only on the distance between the two points and is a piecewise linear function modelled by a marked Poisson process. Simulation of the resulting posterior using a MetropolisHastings algorithm in the “conventional ” way involves evaluating ratios of unknown normalising constants. We avoid this problem by applying a new auxiliary variable technique introduced by Møller, Pettitt, Reeves & Berthelsen (2006). In the present setting the auxiliary variable used is an example of a partially ordered Markov point process model.
ClassSpecific Tests of Spatial Segregation Based on Nearest Neighbor Contingency Tables
, 2008
"... The spatial interaction between two or more classes (or species) has important consequences in many fields and might cause multivariate clustering patterns such as segregation or association. The spatial pattern of segregation occurs when members of a class tend to be found near members of the same ..."
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The spatial interaction between two or more classes (or species) has important consequences in many fields and might cause multivariate clustering patterns such as segregation or association. The spatial pattern of segregation occurs when members of a class tend to be found near members of the same class (i.e., conspecifics), while association occurs when members of a class tend to be found near members of the other class or classes. These patterns can be tested using a nearest neighbor contingency table (NNCT). The null hypothesis is randomness in the nearest neighbor (NN) structure, which may result from — among other patterns — random labeling (RL) or complete spatial randomness (CSR) of points from two or more classes (which is called CSR independence, henceforth). In this article, we consider Dixon’s classspecific tests of segregation and introduce a new classspecific test, which is a new decomposition of Dixon’s overall chisquare segregation statistic. We demonstrate that the tests we consider provide information on different aspects of the spatial interaction between the classes and are conditional under the CSR independence pattern, but not under the RL pattern. We analyze the distributional properties and prove the consistency of these tests; compare the empirical significant levels (Type I error rates) and empirical power estimates of the tests using extensive Monte Carlo simulations. We demonstrate that the new classspecific tests also have comparable performance with the currently available tests based on NNCTs in terms of Type I error and power. For illustrative purposes, we use three example data sets. We also provide guidelines for using these tests.