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Detecting Features in Spatial Point Processes with . . .
, 1995
"... We consider the problem of detecting features in spatial point processes in the presence of substantial clutter. One example is the detection of mine elds using reconnaissance aircraft images that erroneously identify many objects that are not mines. Another is the detection of seismic faults on the ..."
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Cited by 81 (31 self)
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We consider the problem of detecting features in spatial point processes in the presence of substantial clutter. One example is the detection of mine elds using reconnaissance aircraft images that erroneously identify many objects that are not mines. Another is the detection of seismic faults on the basis of earthquake catalogs: earthquakes tend to be clustered close to the faults, but there are many that are farther away. Our solution uses modelbased clustering based on a mixture model for the process, in which features are assumed to generate points according to highly linear multivariate normal densities, and the clutter arises according to a spatial Poisson process. Very nonlinear features are represented by several highly linear multivariate normal densities, giving a piecewise linear representation. The model is estimated in two stages. In the rst stage, hierarchical modelbased clustering is used to provide a rst estimate of the features. In the second stage, this clustering is re ned using the EM algorithm. The number of features is found using an approximation to the posterior probability of each number of features. For the minefield
Practical maximum pseudolikelihood for spatial point patterns
 Australian and New Zealand Journal of Statistics
, 2000
"... This paper describes a technique for computing approximate maximum pseudolikelihood estimates of the parameters of a spatial point process. The method is an extension of Berman & Turner’s (1992) device for maximizing the likelihoods of inhomogeneous spatial Poisson processes. For a very wide class o ..."
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Cited by 45 (7 self)
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This paper describes a technique for computing approximate maximum pseudolikelihood estimates of the parameters of a spatial point process. The method is an extension of Berman & Turner’s (1992) device for maximizing the likelihoods of inhomogeneous spatial Poisson processes. For a very wide class of spatial point process models the likelihood is intractable, while the pseudolikelihood is known explicitly, except for the computation of an integral over the sampling region. Approximation of this integral by a finite sum in a special way yields an approximate pseudolikelihood which is formally equivalent to the (weighted) likelihood of a loglinear model with Poisson responses. This can be maximized using standard statistical software for generalized linear or additive models, provided the conditional intensity of the process takes an ‘exponential family ’ form. Using this approach a wide variety of spatial point process models of Gibbs type can be fitted rapidly, incorporating spatial trends, interaction between points, dependence on spatial covariates, and mark information. Key words: areainteraction process; Berman–Turner device; Dirichlet tessellation; edge effects; generalized additive models; generalized linear models; Gibbs point processes; GLIM; hard core process; inhomogeneous point process; marked point processes; Markov spatial point processes; Ord’s process; pairwise interaction; profile pseudolikelihood; spatial clustering; soft core process; spatial trend; SPLUS; Strauss process; Widom–Rowlinson model. 1.
Non and SemiParametric Estimation of Interaction in Inhomogeneous Point Patterns
, 2000
"... We develop methods for analysing the `interaction' or dependence between points in a spatial point pattern, when the pattern is spatially inhomogeneous. Completely nonparametric study of interactions is possible using an analogue of the Kfunction. Alternatively one may assume a semiparametric mo ..."
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Cited by 43 (17 self)
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We develop methods for analysing the `interaction' or dependence between points in a spatial point pattern, when the pattern is spatially inhomogeneous. Completely nonparametric study of interactions is possible using an analogue of the Kfunction. Alternatively one may assume a semiparametric model in which a (parametrically specified) homogeneous Markov point process is subjected to (nonparametric) inhomogeneous independent thinning. The effectiveness of these approaches is tested on datasets representing the positions of trees in forests.
Predicting the location of northern goshawk nests: modeling the spatial dependency between nest locations and forest structure
, 2004
"... Northern goshawks interact with each other and their environment in a spatially dependent manner. However, finding the location of active goshawk nests (e.g. where eggs are laid) in a given year is difficult due to the secretive nature of the hawks in their forest environment, their annually variabl ..."
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Cited by 2 (0 self)
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Northern goshawks interact with each other and their environment in a spatially dependent manner. However, finding the location of active goshawk nests (e.g. where eggs are laid) in a given year is difficult due to the secretive nature of the hawks in their forest environment, their annually variable attempts at nesting, and the extent of the area within a home range where they will nest. We used a Gibbsian pairwise potential model to describe the spatial dependency (1) among nest locations influenced by territoriality and (2) between nest locations and the environment for a large population of goshawks on the Kaibab National Forest’s (NNF) North Kaibab Ranger District (NKRD). Nest locations in a given year were regularly distributed at a minimum distance of 1.6 km between active nests; however, as the spatial scale increased (i.e. as distance between the nests increased), the degree of regularity decreased. Important forest predictors for nest locations included canopy closure, total basal area, proportion of basal area in ponderosa pine, spruce, fir, and aspen, maximum height of the understory vegetation, and presence/absence of seedlings and saplings. The probability of an occurrence of an active nest within a 10m × 10m area was modeled using logistic regression. Spatial analysis, using nest spacing and habitat variables, indicated that potential active nest locations were abundant and randomly distributed throughout the NKRD. This supports the supposition that the availability of locations with high potential for nests is not limiting the goshawk population on the study area. Instead, territoriality, and what appear to be noncompressible territories, sets the upper limit to the nesting population. Ultimate choice of nest location was probably constrained by the
Aspects Of Spatial Statistics, Stochastic Geometry And Markov Chain Monte Carlo Methods
, 1999
"... ..."
Bayesian Modeling of Continuously Marked Spatial Point Patterns
"... Many analyses of continuously marked spatial point patterns assume that the density of points, with differing marks, is identical. However, as noted in the originative paper of Goulard et al. (1996), such an assumption is not realistic in many situations. For example, a stand of forest may have many ..."
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Cited by 2 (1 self)
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Many analyses of continuously marked spatial point patterns assume that the density of points, with differing marks, is identical. However, as noted in the originative paper of Goulard et al. (1996), such an assumption is not realistic in many situations. For example, a stand of forest may have many more small trees than large, hence the model should allow for a higher density of points with small marks. In addition, as suggested by Ogata & Tanemura (1985), the interaction between points should be a function of their mark, allowing, for example, the range of interaction for large trees to exceed that of smaller trees. The aforementioned articles use frequentist inferential techniques, but interval estimation presents difficulties due to the complex distributional properties of the estimates. We suggest the use of Bayesian inferential techniques. Although a Bayesian approach requires a complex, computational implementation of (reversible jump) MCMC methodology, it enables a wide variety of inferences (including interval estimation). We demonstrate our approach by analyzing the well known Norway spruce dataset. Keywords: Markov chain Monte Carlo (MCMC), reversible jump MCMC, pairwise interacting point process, mark chemical activity function 1 Figure 1: Location of n = 134 Norway spruce trees in a 56 × 38 meter field.
Modeling smallscale spatial interaction of shortgrass prairie species
, 1997
"... Native grasses interact spatially with themselves and their environment and can therefore be thought of as a system of dependent random variables. One method of modeling the spatial dependence of a multispecies population is a Gibbsian pairwise potential model. Since natural selection operates at t ..."
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Native grasses interact spatially with themselves and their environment and can therefore be thought of as a system of dependent random variables. One method of modeling the spatial dependence of a multispecies population is a Gibbsian pairwise potential model. Since natural selection operates at the level of individual plants, the information obtained from such a model should provide a greater understanding of the intraspecific interactions in plant populations, while providing a theoretical basis for determining a plants ' 'competitive zone ' of influence. In this paper we fit a pairwise potential model to describe the spatial dependency of dominant grasses and forbs measured on a 1.5 x 1.5 m study plot located on a shortgrass prairie site near Fort Collins, Colorado. Dominant grasses included blue grama (Bouteloua gracilis), western wheatgrass (Agropyron smithii), Indian ricegrass (Oryzopsis hymenoides), and needleandthread grass (Stipa comata). Procedures for introducing spatial heterogeneity in the model is also