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38
Shot noise Cox processes
 Advances in Applied Probability 35
, 2003
"... We introduce a new class of Cox cluster processes called generalised shotnoise Cox processes (GSNCPs), which extends the definition of shot noise Cox processes (SNCPs) in two directions: the point process which drives the shot noise is not necessarily Poisson, and the kernel of the shot noise can be ..."
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Cited by 23 (6 self)
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We introduce a new class of Cox cluster processes called generalised shotnoise Cox processes (GSNCPs), which extends the definition of shot noise Cox processes (SNCPs) in two directions: the point process which drives the shot noise is not necessarily Poisson, and the kernel of the shot noise can be random. Thereby a very large class of models for aggregated or clustered point patterns is obtained. Due to the structure of GSNCPs, a number of useful results can be established. We focus first on deriving summary statistics for GSNCPs and next on how to make simulation for GSNCPs. Particularly, results for first and second order moment measures, reduced Palm distributions, the Jfunction, simulation with or without edge effects, and conditional simulation of the intensity function driving a GSNCP are given. Our results are exemplified for special important cases of GSNCPs, and we discuss the relation to corresponding results for SNCPs.
Residual analysis for spatial point processes (with discussion
 Journal of the Royal Statistical Society (series B
, 2005
"... [Read before The Royal Statistical Society at a meeting organized by the Research Section on ..."
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Cited by 20 (5 self)
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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
"... 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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Cited by 10 (3 self)
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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
Twostep estimation for inhomogeneous spatial point processes
 In preparation
, 2007
"... processes ..."
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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Cited by 8 (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),
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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Cited by 3 (2 self)
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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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Cited by 3 (2 self)
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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.
Inhomogeneous Spatial Point Processes By Location Dependent Scaling
 IEEE Transactions on Software Engineering
, 1984
"... A new class of models for inhomogeneous spatial point processes is introduced. ..."
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Cited by 2 (1 self)
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A new class of models for inhomogeneous spatial point processes is introduced.