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## Point Processes (point + process)
Kinds of Point Processes
## Selected Abstracts## A Mixture Point Process for Repeated Failure Times, with an Application to a Recurrent Disease BIOMETRICAL JOURNAL, Issue 7 2003O. PonsAbstract We present a model that describes the distribution of recurring times of a disease in presence of covariate effects. After a first occurrence of the disease in an individual, the time intervals between successive cases are supposed to be independent and to be a mixture of two distributions according to the issue of the previous treatment. Both sub-distributions of the model and the mixture proportion are allowed to involve covariates. Parametric inference is considered and we illustrate the methods with data of a recurrent disease and with simulations, using piecewise constant baseline hazard functions. [source] ## Estimating the Intensity of a Spatial Point Process from Locations Coarsened by Incomplete Geocoding BIOMETRICS, Issue 1 2008Dale L. ZimmermanSummary The estimation of spatial intensity is an important inference problem in spatial epidemiologic studies. A standard data assimilation component of these studies is the assignment of a geocode, that is, point-level spatial coordinates, to the address of each subject in the study population. Unfortunately, when geocoding is performed by the standard automated method of street-segment matching to a georeferenced road file and subsequent interpolation, it is rarely completely successful. Typically, 10,30% of the addresses in the study population, and even higher percentages in particular subgroups, fail to geocode, potentially leading to a selection bias, called geographic bias, and an inefficient analysis. Missing-data methods could be considered for analyzing such data; however, because there is almost always some geographic information coarser than a point (e.g., a Zip code) observed for the addresses that fail to geocode, a coarsened-data analysis is more appropriate. This article develops methodology for estimating spatial intensity from coarsened geocoded data. Both nonparametric (kernel smoothing) and likelihood-based estimation procedures are considered. Substantial improvements in the estimation quality of coarsened-data analyses relative to analyses of only the observations that geocode are demonstrated via simulation and an example from a rural health study in Iowa. [source] ## Modelling Tree Roots in Mixed Forest Stands by Inhomogeneous Marked Gibbs Point Processes BIOMETRICAL JOURNAL, Issue 3 2009Stefanie EckelAbstract The aim of the paper is to apply point processes to root data modelling. We propose a new approach to parametric inference when the data are inhomogeneous replicated marked point patterns. We generalize Geyer's saturation point process to a model, which combines inhomogeneity, marks and interaction between the marked points. Furthermore, the inhomogeneity influences the definition of the neighbourhood of points. Using the maximum pseudolikelihood method, this model is then fitted to root data from mixed stands of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.) to quantify the degree of root aggregation in such mixed stands. According to the analysis there is no evidence that the two root systems are not independent. [source] ## Inference for Clustered Inhomogeneous Spatial Point Processes BIOMETRICS, Issue 2 2009P. A. HenrysSummary We propose a method to test for significant differences in the levels of clustering between two spatial point processes (cases and controls) while taking into account differences in their first-order intensities. The key advance on earlier methods is that the controls are not assumed to be a Poisson process. Inference and diagnostics are based around the inhomogeneous K -function with confidence envelopes obtained from either resampling events in a nonparametric bootstrap approach, or simulating new events as in a parametric bootstrap. Methods developed are demonstrated using the locations of adult and juvenile trees in a tropical forest. A simulation study briefly examines the accuracy and power of the inferential procedures. [source] ## Point process methodology for on-line spatio-temporal disease surveillance ENVIRONMETRICS, Issue 5 2005Peter DiggleAbstract We formulate the problem of on-line spatio-temporal disease surveillance in terms of predicting spatially and temporally localised excursions over a pre-specified threshold value for the spatially and temporally varying intensity of a point process in which each point represents an individual case of the disease in question. Our point process model is a non-stationary log-Gaussian Cox process in which the spatio-temporal intensity, ,(x,t), has a multiplicative decomposition into two deterministic components, one describing purely spatial and the other purely temporal variation in the normal disease incidence pattern, and an unobserved stochastic component representing spatially and temporally localised departures from the normal pattern. We give methods for estimating the parameters of the model, and for making probabilistic predictions of the current intensity. We describe an application to on-line spatio-temporal surveillance of non-specific gastroenteric disease in the county of Hampshire, UK. The results are presented as maps of exceedance probabilities, P{R(x,t)c|data}, where R(x,t) is the current realisation of the unobserved stochastic component of ,(x,t) and c is a pre-specified threshold. These maps are updated automatically in response to each day's incident data using a web-based reporting system. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Spatial point-process statistics: concepts and application to the analysis of lead contamination in urban soil, ENVIRONMETRICS, Issue 4 2005Christian WalterAbstract This article explores the use of spatial point-process analysis as an aid to describe topsoil lead distribution in urban environments. The data used were collected in Glebe, an inner suburb of Sydney. The approach focuses on the locations of punctual events defining a point pattern, which can be statistically described through local intensity estimates and between-point distance functions. F -, G - and K -surfaces of a marked spatial point pattern were described and used to estimate nearest distance functions over a sliding band of quantiles belonging to the marking variable. This provided a continuous view of the point pattern properties as a function of the marking variable. Several random fields were simulated by selecting points from random, clustered or regular point processes and diffusing them. Recognition of the underlying point process using variograms derived from dense sampling was difficult because, structurally, the variograms were very similar. Point-event distance functions were useful complimentary tools that, in most cases, enabled clear recognition of the clustered processes. Spatial sampling quantile point pattern analysis was defined and applied to the Glebe data set. The analysis showed that the highest lead concentrations were strongly clustered. The comparison of this data set with the simulation confidence limits of a Poisson process, a short-radius clustered point process and a geostatistical simulation showed a random process for the third quartile of lead concentrations but strong clustering for the data in the upper quartile. Thus the distribution of topsoil lead concentrations over Glebe may have resulted from several contamination processes, mainly from regular or random processes with large diffusion ranges and short-range clustered processes for the hot spots. Point patterns with the same characteristics as the Glebe experimental pattern could be generated by separate additive geostatistical simulation. Spatial sampling quantile point patterns statistics can, in an easy and accurate way, be used complementarily with geostatistical methods. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## A probabilistic two-scale model for high-cycle fatigue life predictions FATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 3 2005C. DOUDARDABSTRACT It is proposed to develop and identify a probabilistic two-scale model for HCF that accounts for the failure of samples, but also for the thermal effects during cyclic loadings in a unified framework. The probabilistic model is based on a Poisson point process. Within the weakest link theory, the model corresponds to a Weibull law for the fatigue limits. The thermal effects can be described if one considers the same hypotheses apart from the weakest link assumption. A method of identification is proposed and uses temperature measurements to identify the scatter in an S/N curve. The validation of the model is obtained by predicting S/N curves for different effective volumes of a dual-phase steel. [source] ## Moment estimation for statistics from marked point processes JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2001Dimitris N. PolitisIn spatial statistics the data typically consist of measurements of some quantity at irregularly scattered locations; in other words, the data form a realization of a marked point process. In this paper, we formulate subsampling estimators of the moments of general statistics computed from marked point process data, and we establish their L2 -consistency. The variance estimator in particular can be used for the construction of confidence intervals for estimated parameters. A practical data-based method for choosing a subsampling parameter is given and illustrated on a data set. Finite sample simulation examples are also presented. [source] ## A percolating hard sphere model RANDOM STRUCTURES AND ALGORITHMS, Issue 2 2009Codina CotarAbstract Given a homogeneous Poisson point process in ,d, Häggström and Meester (Random Struct Algorithms 9 (1996) 295,315) asked whether it is possible to place spheres (of differing radii) centred at the points, in a translation-invariant way, so that the spheres do not overlap but there is an unbounded component of touching spheres. We prove that the answer is yes in sufficiently high dimension. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009 [source] ## Poisson convergence in the restricted k -partitioning problem RANDOM STRUCTURES AND ALGORITHMS, Issue 4 2007Anton BovierAbstract The randomized k -number partitioning problem is the task to distribute N i.i.d. random variables into k groups in such a way that the sums of the variables in each group are as similar as possible. The restricted k -partitioning problem refers to the case where the number of elements in each group is fixed to N/k. In the case k = 2 it has been shown that the properly rescaled differences of the two sums in the close to optimal partitions converge to a Poisson point process, as if they were independent random variables. We generalize this result to the case k > 2 in the restricted problem and show that the vector of differences between the k sums converges to a k - 1-dimensional Poisson point process. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007 [source] ## Some notes on poisson limits for empirical point processes THE CANADIAN JOURNAL OF STATISTICS, Issue 3 2009André DabrowskiAbstract The authors define the scaled empirical point process. They obtain the weak limit of these point processes through a novel use of a dimension-free method based on the convergence of compensators of multiparameter martingales. The method extends previous results in several directions. They obtain limits at points where the density may be zero, but has regular variation. The joint limit of the empirical process evaluated at distinct points is given by independent Poisson processes. They provide applications both to nearest-neighbour density estimation in high dimensions, and to the asymptotic behaviour of multivariate extremes such as those arising from bivariate normal copulas. The Canadian Journal of Statistics 37: 347,360; 2009 © 2009 Statistical Society of Canada Les auteurs définissent un processus ponctuel empirique normalisé. Ils obtiennent une limite faible de ces processus ponctuels grâce à l'utilisation novatrice d'une méthode indépendante de la dimension basée sur la convergence des compensateurs de martingales à plusieurs paramètres. La méthode généralise des résultats précédents de différentes façons. Ils obtiennent des limites à des points où la densité peut être égale à 0, mais qui est à variation régulière. La limite conjointe du processus empirique évalué à des points distincts est représentée par des processus de Poisson indépendants. Les auteurs présentent deux applications, l'une sur l'estimation de densité de dimension élevée basée sur le plus proche voisin et l'autre sur le comportement asymptotique des extrêmes multidimensionnels provenant de copules normales bidimensionnelles. La revue canadienne de statistique 37: 347,360; 2009 © 2009 Société statistique du Canada [source] ## Modelling Tree Roots in Mixed Forest Stands by Inhomogeneous Marked Gibbs Point Processes BIOMETRICAL JOURNAL, Issue 3 2009Stefanie EckelAbstract The aim of the paper is to apply point processes to root data modelling. We propose a new approach to parametric inference when the data are inhomogeneous replicated marked point patterns. We generalize Geyer's saturation point process to a model, which combines inhomogeneity, marks and interaction between the marked points. Furthermore, the inhomogeneity influences the definition of the neighbourhood of points. Using the maximum pseudolikelihood method, this model is then fitted to root data from mixed stands of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.) to quantify the degree of root aggregation in such mixed stands. According to the analysis there is no evidence that the two root systems are not independent. [source] ## Cluster Pattern Detection in Spatial Data Based on Monte Carlo Inference BIOMETRICAL JOURNAL, Issue 4 2007Radu Stefan StoicaAbstract Clusters in a data point field exhibit spatially specified regions in the observation window. The method proposed in this paper addresses the cluster detection problem from the perspective of detection of these spatial regions. These regions are supposed to be formed of overlapping random disks driven by a marked point process. The distribution of such a process has two components. The first is related to the location of the disks in the field of observation and is defined as an inhomogeneous Poisson process. The second one is related to the interaction between disks and is constructed by the superposition of an area-interaction and a pairwise interaction processes. The model is applied on spatial data coming from animal epidemiology. The proposed method tackles several aspects related to cluster pattern detection: heterogeneity of data, smoothing effects, statistical descriptors, probability of cluster presence, testing for the cluster presence. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Nonparametric One-way Analysis of Variance of Replicated Bivariate Spatial Point Patterns BIOMETRICAL JOURNAL, Issue 1 2004Sabine LandauAbstract A common problem in neuropathological studies is to assess the spatial patterning of cells on tissue sections and to compare spatial patterning between disorder groups. For a single cell type, the cell positions constitute a univariate point process and interest focuses on the degree of spatial aggregation. For two different cell types, the cell positions constitute a bivariate point process and the degree of spatial interaction between the cell types is of interest. We discuss the problem of analysing univariate and bivariate spatial point patterns in the one-way design where cell patterns have been obtained for groups of subjects. A bootstrapping procedure to perform a nonparametric one-way analysis of variance of the spatial aggregation of a univariate point process has been suggested by Diggle, Lange and Bene, (1991). We extend their replication-based approach to allow the comparison of the spatial interaction of two cell types between groups, to include planned comparisons (contrasts) and to assess whole groups against complete spatial randomness and spatial independence. We also accommodate several replicate tissue sections per subject. An advantage of our approach is that it can be applied when processes are not stationary, a common problem in brain tissue sections since neurons are arranged in cortical layers. We illustrate our methods by applying them to a neuropathological study to investigate abnormalities in the functional relationship between neurons and astrocytes in HIV associated dementia. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## A Model-Based Approach for Making Ecological Inference from Distance Sampling Data BIOMETRICS, Issue 1 2010Devin S. JohnsonSummary We consider a fully model-based approach for the analysis of distance sampling data. Distance sampling has been widely used to estimate abundance (or density) of animals or plants in a spatially explicit study area. There is, however, no readily available method of making statistical inference on the relationships between abundance and environmental covariates. Spatial Poisson process likelihoods can be used to simultaneously estimate detection and intensity parameters by modeling distance sampling data as a thinned spatial point process. A model-based spatial approach to distance sampling data has three main benefits: it allows complex and opportunistic transect designs to be employed, it allows estimation of abundance in small subregions, and it provides a framework to assess the effects of habitat or experimental manipulation on density. We demonstrate the model-based methodology with a small simulation study and analysis of the Dubbo weed data set. In addition, a simple ad hoc method for handling overdispersion is also proposed. The simulation study showed that the model-based approach compared favorably to conventional distance sampling methods for abundance estimation. In addition, the overdispersion correction performed adequately when the number of transects was high. Analysis of the Dubbo data set indicated a transect effect on abundance via Akaike's information criterion model selection. Further goodness-of-fit analysis, however, indicated some potential confounding of intensity with the detection function. [source] ## The Econometrics of Ultra-high-frequency Data ECONOMETRICA, Issue 1 2000Robert F. EngleUltra-high-frequency data is defined to be a full record of transactions and their associated characteristics. The transaction arrival times and accompanying measures can be analyzed as marked point processes. The ACD point process developed by Engle and Russell (1998) is applied to IBM transactions arrival times to develop semiparametric hazard estimates and conditional intensities. Combining these intensities with a GARCH model of prices produces ultra-high-frequency measures of volatility. Both returns and variances are found to be negatively influenced by long durations as suggested by asymmetric information models of market micro-structure. [source] ## Spatio-temporal point process filtering methods with an application ENVIRONMETRICS, Issue 3-4 2010ena FrcalováAbstract The paper deals with point processes in space and time and the problem of filtering. Real data monitoring the spiking activity of a place cell of hippocampus of a rat moving in an environment are evaluated. Two approaches to the modelling and methodology are discussed. The first one (known from literature) is based on recursive equations which enable to describe an adaptive system. Sequential Monte Carlo methods including particle filter algorithm are available for the solution. The second approach makes use of a continuous time shot-noise Cox point process model. The inference of the driving intensity leads to a nonlinear filtering problem. Parametric models support the solution by means of the Bayesian Markov chain Monte Carlo methods, moreover the Cox model enables to detect adaptivness. Model selection is discussed, numerical results are presented and interpreted. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Spatial,temporal marked point processes: a spectrum of stochastic models ENVIRONMETRICS, Issue 3-4 2010Eric RenshawAbstract Many processes that develop through space and time do so in response not only to their own individual growth mechanisms but also in response to interactive pressures induced by their neighbours. The growth of trees in a forest which compete for light and nutrient resources, for example, provides a classic illustration of this general spatial,temporal growth-interaction process. Not only has its mathematical representation proved to be a powerful tool in the study and analysis of marked point patterns since it may easily be simulated, but it has also been shown to be highly flexible in terms of its application since it is robust with respect to incorrect choice of model selection. Moreover, it is highly amenable to maximum likelihood and least squares parameter estimation techniques. Currently the algorithm comprises deterministic growth and interaction coupled with a stochastic arrival and departure mechanism. So for systems with a fixed number of particles there is an inherent lack of randomness. A variety of different stochastic approaches are therefore presented, from the exact event,time model through to the associated stochastic differential equation, taking in time-increment and Tau- and Langevin-Leaping approximations en route. The main algorithm is illustrated through application to forest management and high-intensity packing of hard particle systems, and comparisons are made with the established force biased approach. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Spatial point-process statistics: concepts and application to the analysis of lead contamination in urban soil, ENVIRONMETRICS, Issue 4 2005Christian WalterAbstract This article explores the use of spatial point-process analysis as an aid to describe topsoil lead distribution in urban environments. The data used were collected in Glebe, an inner suburb of Sydney. The approach focuses on the locations of punctual events defining a point pattern, which can be statistically described through local intensity estimates and between-point distance functions. F -, G - and K -surfaces of a marked spatial point pattern were described and used to estimate nearest distance functions over a sliding band of quantiles belonging to the marking variable. This provided a continuous view of the point pattern properties as a function of the marking variable. Several random fields were simulated by selecting points from random, clustered or regular point processes and diffusing them. Recognition of the underlying point process using variograms derived from dense sampling was difficult because, structurally, the variograms were very similar. Point-event distance functions were useful complimentary tools that, in most cases, enabled clear recognition of the clustered processes. Spatial sampling quantile point pattern analysis was defined and applied to the Glebe data set. The analysis showed that the highest lead concentrations were strongly clustered. The comparison of this data set with the simulation confidence limits of a Poisson process, a short-radius clustered point process and a geostatistical simulation showed a random process for the third quartile of lead concentrations but strong clustering for the data in the upper quartile. Thus the distribution of topsoil lead concentrations over Glebe may have resulted from several contamination processes, mainly from regular or random processes with large diffusion ranges and short-range clustered processes for the hot spots. Point patterns with the same characteristics as the Glebe experimental pattern could be generated by separate additive geostatistical simulation. Spatial sampling quantile point patterns statistics can, in an easy and accurate way, be used complementarily with geostatistical methods. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## A hybrid search combining interior point methods and metaheuristics for 0,1 programming INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 6 2002Agnès PlateauOur search deals with methods hybridizing interior point processes and metaheuristics for solving 0,1 linear programs. This paper shows how metaheuristics can take advantage of a sequence of interior points generated by an interior point method. After introducing our work field, we present our hybrid search which generates a diversified population. Next, we explain the whole method combining the solutions encountered in the previous phase through a path relinking template. Computational experiments are reported on 0,1 multiconstraint knapsack problems. [source] ## Residual analysis for spatial point processes (with discussion) JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 5 2005A. BaddeleySummary., We define residuals for point process models fitted to spatial point pattern data, and we propose diagnostic plots based on them. The residuals apply to any point process model that has a conditional intensity; the model may exhibit spatial heterogeneity, interpoint interaction and dependence on spatial covariates. Some existing ad hoc methods for model checking (quadrat counts, scan statistic, kernel smoothed intensity and Berman's diagnostic) are recovered as special cases. Diagnostic tools are developed systematically, by using an analogy between our spatial residuals and the usual residuals for (non-spatial) generalized linear models. The conditional intensity , plays the role of the mean response. This makes it possible to adapt existing knowledge about model validation for generalized linear models to the spatial point process context, giving recommendations for diagnostic plots. A plot of smoothed residuals against spatial location, or against a spatial covariate, is effective in diagnosing spatial trend or co-variate effects. Q,Q -plots of the residuals are effective in diagnosing interpoint interaction. [source] ## Moment estimation for statistics from marked point processes JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2001Dimitris N. PolitisIn spatial statistics the data typically consist of measurements of some quantity at irregularly scattered locations; in other words, the data form a realization of a marked point process. In this paper, we formulate subsampling estimators of the moments of general statistics computed from marked point process data, and we establish their L2 -consistency. The variance estimator in particular can be used for the construction of confidence intervals for estimated parameters. A practical data-based method for choosing a subsampling parameter is given and illustrated on a data set. Finite sample simulation examples are also presented. [source] ## The Term Structure of Simple Forward Rates with Jump Risk MATHEMATICAL FINANCE, Issue 3 2003Paul GlassermanThis paper characterizes the arbitrage-free dynamics of interest rates, in the presence of both jumps and diffusion, when the term structure is modeled through simple forward rates (i.e., through discretely compounded forward rates evolving continuously in time) or forward swap rates. Whereas instantaneous continuously compounded rates form the basis of most traditional interest rate models, simply compounded rates and their parameters are more directly observable in practice and are the basis of recent research on "market models." We consider very general types of jump processes, modeled through marked point processes, allowing randomness in jump sizes and dependence between jump sizes, jump times, and interest rates. We make explicit how jump and diffusion risk premia enter into the dynamics of simple forward rates. We also formulate reasonably tractable subclasses of models and provide pricing formulas for some derivative securities, including interest rate caps and options on swaps. Through these formulas, we illustrate the effect of jumps on implied volatilities in interest rate derivatives. [source] ## Non-homogeneous infinitely many sites discrete-time model with exact coalescent MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2010Adam BobrowskiAbstract Kingman's coalescent is among the most fertile concepts in mathematical population genetics. However, it only approximates the exact coalescent process associated with the Wright,Fisher model, in which the ancestry of a sample does not have to be a binary tree. The distinction between the approximate and exact coalescent becomes important when population size is small and time has to be measured in discrete units (generations). In the present paper, we explore the exact coalescent, with mutations following the infinitely many sites model. The methods used involve random point processes and generating functionals. This allows obtaining joint distributions of segregating sites in arbitrary intervals or collections of intervals, and generally in arbitrary Borel subsets of two or more chromosomes. Using this framework it is possible to find the moments of the numbers of segregating sites on pairs of chromosomes, as well as the moments of the average of the number of pairwise differences, in the form that is more general than usually. In addition, we demonstrate limit properties of the first two moments under a range of demographic scenarios, including different patterns of population growth. This latter part complements results obtained earlier for Kingman's coalescent. Finally, we discuss various applications, including the analysis of fluctuation experiments, from which mutation rates of biological cells can be inferred. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## On the use of second-order descriptors to predict queueing behavior of MAPs NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 4 2002Allan T. AndersenAbstract The contributions of this paper are the following: We derive a formula for the IDI (Index of Dispersion for Intervals) for the Markovian Arrival Process (MAP). We show that two-state MAPs with identical fundamental rate, IDI and IDC (Index of Dispersion for Counts), define interval stationary point processes that are stochastically equivalent; this is true for the time stationary point processes they define too. Special cases of the two-state MAP are frequently used as source models in the literature. The result shows that, fitting to the rate, IDC and IDI of a source completely determine the interval stationary and time stationary behavior of the two-state model. We give various illustrative numerical examples on the merits in predicting queueing behavior on the basis of first- and second-order descriptors by considering queueing behavior of MAPs with constant fundamental rate and IDC, respectively, constant fundamental rate and IDI. Disturbing results are presented on how different the queueing behavior can be with these descriptors fixed. Even MAPs with NO correlations in the counting process, i.e., IDC(t) = 1 are shown to have very different queueing behavior. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 391,409, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10015 [source] ## GIS and spatial data analysis: Converging perspectives PAPERS IN REGIONAL SCIENCE, Issue 1 2004Michael F. GoodchildGIS; spatial data analysis; spatial modelling; geostatistics; point processes Abstract. This article identifies some of the important developments in GIS and spatial data analysis since the early 1950s. Although GIS and spatial data analysis started out as two more or less separate areas of research and application, they have grown closer together over time. We argue that the two areas meet in the field of geographic information science, with each supporting and adding value to the other. The article starts off providing a critical retrospective of developments over the past 50 years. Subsequently, we reflect on current challenges and speculate about the future. Finally, we comment on the potential for convergence of developments in GIS and spatial data analysis under the rubric of geographic information science (GIScience). [source] ## Some notes on poisson limits for empirical point processes THE CANADIAN JOURNAL OF STATISTICS, Issue 3 2009André DabrowskiAbstract The authors define the scaled empirical point process. They obtain the weak limit of these point processes through a novel use of a dimension-free method based on the convergence of compensators of multiparameter martingales. The method extends previous results in several directions. They obtain limits at points where the density may be zero, but has regular variation. The joint limit of the empirical process evaluated at distinct points is given by independent Poisson processes. They provide applications both to nearest-neighbour density estimation in high dimensions, and to the asymptotic behaviour of multivariate extremes such as those arising from bivariate normal copulas. The Canadian Journal of Statistics 37: 347,360; 2009 © 2009 Statistical Society of Canada Les auteurs définissent un processus ponctuel empirique normalisé. Ils obtiennent une limite faible de ces processus ponctuels grâce à l'utilisation novatrice d'une méthode indépendante de la dimension basée sur la convergence des compensateurs de martingales à plusieurs paramètres. La méthode généralise des résultats précédents de différentes façons. Ils obtiennent des limites à des points où la densité peut être égale à 0, mais qui est à variation régulière. La limite conjointe du processus empirique évalué à des points distincts est représentée par des processus de Poisson indépendants. Les auteurs présentent deux applications, l'une sur l'estimation de densité de dimension élevée basée sur le plus proche voisin et l'autre sur le comportement asymptotique des extrêmes multidimensionnels provenant de copules normales bidimensionnelles. La revue canadienne de statistique 37: 347,360; 2009 © 2009 Société statistique du Canada [source] ## Modelling Tree Roots in Mixed Forest Stands by Inhomogeneous Marked Gibbs Point Processes BIOMETRICAL JOURNAL, Issue 3 2009Stefanie EckelAbstract The aim of the paper is to apply point processes to root data modelling. We propose a new approach to parametric inference when the data are inhomogeneous replicated marked point patterns. We generalize Geyer's saturation point process to a model, which combines inhomogeneity, marks and interaction between the marked points. Furthermore, the inhomogeneity influences the definition of the neighbourhood of points. Using the maximum pseudolikelihood method, this model is then fitted to root data from mixed stands of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.) to quantify the degree of root aggregation in such mixed stands. According to the analysis there is no evidence that the two root systems are not independent. [source] ## A Hypothesis-Free Multiple Scan Statistic with Variable Window BIOMETRICAL JOURNAL, Issue 2 2008L. CucalaAbstract In this article we propose a new technique for identifying clusters in temporal point processes. This relies on the comparision between all the m -order spacings and it is totally independent of any alternative hypothesis. A recursive procedure is introduced and allows to identify multiple clusters independently. This new scan statistic seems to be more efficient than the classical scan statistic for detecting and recovering cluster alternatives. These results have applications in epidemiological studies of rare diseases. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Inference for Clustered Inhomogeneous Spatial Point Processes BIOMETRICS, Issue 2 2009P. A. HenrysSummary We propose a method to test for significant differences in the levels of clustering between two spatial point processes (cases and controls) while taking into account differences in their first-order intensities. The key advance on earlier methods is that the controls are not assumed to be a Poisson process. Inference and diagnostics are based around the inhomogeneous K -function with confidence envelopes obtained from either resampling events in a nonparametric bootstrap approach, or simulating new events as in a parametric bootstrap. Methods developed are demonstrated using the locations of adult and juvenile trees in a tropical forest. A simulation study briefly examines the accuracy and power of the inferential procedures. [source] |