Search results for "Point Process."
showing 10 items of 98 documents
A Three-Dimensional Object Point Process for Detection of Cosmic Filaments
2007
Summary We propose to apply an object point process to delineate filaments of the large scale structure in red shift catalogues automatically. We illustrate the feasibility of the idea on an example of the recent 2dF Galaxy Redshift Survey, describe the procedure and characterize the results.
Detection of spatial disease clusters with LISA functions.
2011
Detection of disease clusters is an important tool in epidemiology that can help to identify risk factors associated with the disease and in understanding its etiology. In this article we propose a method for the detection of spatial clusters where the locations of a set of cases and a set of controls are available. The method is based on local indicators of spatial association functions (LISA functions), particularly on the development of a local version of the product density, which is a second-order characteristic of spatial point processes. The behavior of the method is evaluated and compared with Kulldorff's spatial scan statistic by means of a simulation study. It is shown that the LI…
Conditionally heteroscedastic intensity-dependent marking of log Gaussian Cox processes
2009
Spatial marked point processes are models for systems of points which are randomly distributed in space and provided with measured quantities called marks. This study deals with marking, that is methods of constructing marked point processes from unmarked ones. The focus is density-dependent marking where the local point intensity affects the mark distribution. This study develops new markings for log Gaussian Cox processes. In these markings, both the mean and variance of the mark distribution depend on the local intensity. The mean, variance and mark correlation properties are presented for the new markings, and a Bayesian estimation procedure is suggested for statistical inference. The p…
FLP estimation of semi-parametric models for space-time point processes and diagnostic tools
2015
Abstract The conditional intensity function of a space–time branching model is defined by the sum of two main components: the long-run term intensity and short-run term one. Their simultaneous estimation is a complex issue that usually requires the use of hard computational techniques. This paper deals with a new mixed estimation approach for a particular space–time branching model, the Epidemic Type Aftershock Sequence model. This approach uses a simultaneous estimation of the different model components, alternating a parametric step for estimating the induced component by Maximum Likelihood and a non-parametric estimation step, for the background intensity, by FLP (Forward Predictive Like…
Testing abnormality in the spatial arrangement of cells in the corneal endothelium using spatial point processes
2001
The study of central corneal endothelium morphology is important in Ophthalmology. Some of the pathologies that could compromise endothelial cell morphology are trauma, cataract, surgery, use of contact lenses, corneal dystrophies or degenerations. The quantitative analysis of cell shape and cellular pattern is more sensitive in detecting subtle changes in endothelial morphology than cell density measurement or cell area analysis. In this paper, the morphology of the central cornea, the most important area from the point of view of vision, is studied through an associated bivariate spatial point pattern: the centroids of the cells and the triple points, that is, the points where three diffe…
Second-order diagnostics for space-time point processes with application to seismic events
2008
A diagnostic method for space-time point process is introduced and used to interpret and assess the goodness of fit of particular models to real data such as the seismic ones. The proposed method is founded on the definition of a weighted process and allows to detect second-order features of data, like long-range dependence and fractal behavior, that are not accounted for by the fitted model. Applications to earthquake data are provided. Copyright © 2008 John Wiley & Sons, Ltd.
Intensity estimation for inhomogeneous Gibbs point process with covariates-dependent chemical activity
2014
Recent development of intensity estimation for inhomogeneous spatial point processes with covariates suggests that kerneling in the covariate space is a competitive intensity estimation method for inhomogeneous Poisson processes. It is not known whether this advantageous performance is still valid when the points interact. In the simplest common case, this happens, for example, when the objects presented as points have a spatial dimension. In this paper, kerneling in the covariate space is extended to Gibbs processes with covariates-dependent chemical activity and inhibitive interactions, and the performance of the approach is studied through extensive simulation experiments. It is demonstr…
Mixed Non-Parametric and Parametric Estimation Techniques in R Package etasFLP for Earthquakes’ Description
2017
etasFLP is an R package which fits an epidemic type aftershock sequence (ETAS) model to an earthquake catalog; non-parametric background seismicity can be estimated through a forward predictive likelihood approach, while parametric components of triggered seismicity are estimated through maximum likelihood; estimation steps are alternated until convergence is obtained and for each event the probability of being a background event is estimated. The package includes options which allow its wide use. Methods for plot, summary and profile are defined for the main output class object. The paper provides examples of the package's use with description of the underlying R and Fortran routines.
Local Spatial Log-Gaussian Cox Processes for seismic data
2022
AbstractIn this paper, we propose the use of advanced and flexible statistical models to describe the spatial displacement of earthquake data. The paper aims to account for the external geological information in the description of complex seismic point processes, through the estimation of models with space varying parameters. A local version of the Log-Gaussian Cox processes (LGCP) is introduced and applied for the first time, exploiting the inferential tools in Baddeley (Spat Stat 22:261–295, 2017), estimating the model by the local Palm likelihood. We provide methods and approaches accounting for the interaction among points, typically described by LGCP models through the estimation of th…
A Note on Robust Intensity Estimation for Point Processes
1992
A robust intensity estimator based on independent marking is derived. A simulation study is made to convince that the new estimator works also in such cases where the usual estimators based on the distance methods do not work. Some truncated distributions are derived.