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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 96 (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
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 semiparametr ..."
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Cited by 62 (18 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.
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 cla ..."
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Cited by 61 (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.
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 3 (2 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.
Aspects Of Spatial Statistics, Stochastic Geometry And Markov Chain Monte Carlo Methods
, 1999
"... ..."
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 3 (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
Modeling Correlated Arrival Events with Latent SemiMarkov Processes
"... The analysis of correlated point process data has wide applications, ranging from biomedical research to network analysis. In this work, we model such data as generated by a latent collection of continuoustime binary semiMarkov processes, corresponding to external events appearing and disappear ..."
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The analysis of correlated point process data has wide applications, ranging from biomedical research to network analysis. In this work, we model such data as generated by a latent collection of continuoustime binary semiMarkov processes, corresponding to external events appearing and disappearing. A continuoustime modeling framework is more appropriate for multichannel point process data than a binning approach requiring time discretization, and we show connections between our model and recent ideas from the discretetime literature. We describe an efficient MCMC algorithm for posterior inference, and apply our ideas to both synthetic data and a realworld biometrics application. 1.
Integrating spatial statistics with GIS and remote sensing in designing multiresource inventories The North American Symposium Towards a Unified Framework for Inventory and Monitoring Forest Ecosystem Resources
, 1998
"... AbstractIn order to design an integrated multiresource inventory and monitoring system that evaluates the status and trends of natural resources (forest, rangeland, agriculture, wildlife, hydrology, soils, etc.) baseline data for comparison is needed. These systems are generally complex and it ma ..."
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AbstractIn order to design an integrated multiresource inventory and monitoring system that evaluates the status and trends of natural resources (forest, rangeland, agriculture, wildlife, hydrology, soils, etc.) baseline data for comparison is needed. These systems are generally complex and it may not be wise to select just one or two variables for monitoring purposes. Also, analyzing these variables independently of one another may lead to incorrect conclusion because of their interdependencies. One approach is to model the spatial relationship that exists between key variables. This information can then be used, for example, to identify forest habitat that are either conducive, or deterrent to the presence of ecologically important plant and/or animal species. Techniques commonly used in describing spatial relationships between two or more variables include regression analysis and a variety of spatial and geostatistical procedures such as kriging and cokriging. The
Estimating the Partition Function by Discriminance Sampling
"... Importance sampling (IS) and its variant, annealed IS (AIS) have been widely used for estimating the partition function in graphical models, such as Markov random fields and deep generative models. However, IS tends to underestimate the partition function and is subject to high variance when th ..."
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Importance sampling (IS) and its variant, annealed IS (AIS) have been widely used for estimating the partition function in graphical models, such as Markov random fields and deep generative models. However, IS tends to underestimate the partition function and is subject to high variance when the proposal distribution is more peaked than the target distribution. On the other hand, “reverse ” versions of IS and AIS tend to overestimate the partition function, and degenerate when the target distribution is more peaked than the proposal distribution. In this work, we present a simple, general method that gives much more reliable and robust estimates than either IS (AIS) or reverse IS (AIS). Our method works by converting the estimation problem into a simple classification problem that discriminates between the samples drawn from the target and the proposal. We give extensive theoretical and empirical justification; in particular, we show that an annealed version of our method significantly outperforms both AIS and reverse AIS as proposed by Burda et al. (2015), which has been the stateoftheart for likelihood evaluation in deep generative models. 1