Quick inference for log Gaussian Cox processes with non-stationary underlying random fields

For point patterns observed in natura, spatial heterogeneity is more the rule than the exception. In numerous applications, this can be mathematically handled by the flexible class of log Gaussian Cox processes (LGCPs); in brief, a LGCP is a Cox process driven by an underlying log Gaussian random field (log GRF). This allows the representation of point aggregation, point vacuum and intermediate situations, with more or less rapid transitions between these different states depending on the properties of GRF. Very often, the covariance function of the GRF is assumed to be stationary. In this article, we give two examples where the sizes (that is, the number of points) and the spatial extents of point clusters are allowed to vary in space. To tackle such features, we propose parametric and semiparametric models of non-stationary LGCPs where the non-stationarity is included in both the mean function and the covariance function of the GRF. Thus, in contrast to most other work on inhomogeneous LGCPs, second-order intensity-reweighted stationarity is not satisfied and the usual two step procedure for parameter estimation based on e.g. composite likelihood does not easily apply. Instead we propose a fast three step procedure based on composite likelihood. We apply our modelling and estimation framework to analyse datasets dealing with fish aggregation in a reservoir and with dispersal of biological particles

On spatial and spatio-temporal multi-structure point process models

Spatial and spatio-temporal single-structure point process models are widely used in epidemiology, biology, ecology, seismology... . However, most natural phenomena present multiple interaction structure or exhibit dependence at multiple scales in space and/or time, leading to define new spatial and spatio-temporal multi-structure point process models. In this paper, we investigate and review such multi-structure point process models mainly based on Gibbs and Cox processes

Analyzing dependence between point processes in time using IndTestPP

The need to analyze the dependence between two or more point processes in time appears in many modeling problems related to the occurrence of events, such as the occurrence of climate events at different spatial locations or synchrony detection in spike train analysis. The package IndTestPP provides a general framework for all the steps in this type of analysis, and one of its main features is the implementation of three families of tests to study independence given the intensities of the processes, which are not only useful to assess independence but also to identify factors causing dependence. The package also includes functions for generating different types of dependent point processes, and implements computational statistical inference tools using them. An application to characterize the dependence between the occurrence of extreme heat events in three Spanish locations using the package is shown

Statistical methods for spatial screening

Military bases that have been used for weapon-testing and training usually are contaminated with unexploded ordnance (UXO). These sites can be returned to public use only after UXO remediation. The cleaning-up procedure is usually very expensive and time-consuming. This demands statistical tools to provide more effective sampling strategy and to characterize the UXO distribution. Based on the physical characteristics of UXO deposition, we adopt a simplified Neyman-Scott process to model the UXO distribution. A line transect survey is used to collect data on one coordinate of individual object locations. Two-stage (global and local) sampling strategy is applied to screen the contaminated site. In the global sampling, the estimators of the cluster intensity, mean cluster size and cluster dispersion are provided. The theoretical variance estimators of all the cluster parameters are also given. Simulation studies show that all the parameter estimates perform well and their theoretical variance estimates are reasonably close to their corresponding sample variances. In the local sampling, an inclusion region for covering all the unobserved objects in a cluster is proposed. Its asymptotic coverage property is given and proved. Simulation studies show the actual coverage of the inclusion region is very close to the nominal level