arXiv subjects

Jorge Mateu

Publications and source records attributed to Jorge Mateu.

47 records · Page 3Linked to original sources

arXiv2018

Resample-smoothing of Voronoi intensity estimators

Voronoi intensity estimators, which are non-parametric estimators for intensity functions of point processes, are both parameter-free and adaptive; the intensity estimate at a given location is given by the reciprocal size of the Voronoi/Dirichlet cell containing that location. Their major drawback, however, is that they tend to under-smooth the data in regions where the point density of the observed point pattern is high and over-smooth in regions where the point density is low. To remedy this problem, i.e. to find some middle-ground between over- and under-smoothing, we propose an additional smoothing technique for Voronoi intensity estimators for point processes in arbitrary metric spaces, which is based on repeated independent thinnings of the point process/pattern. Through a simulation study we show that our resample-smoothing technique improves the estimation significantly. In addition, we study statistical properties such as unbiasedness and variance, and propose a rule-of-thumb and a data-driven cross-validation approach to choose the amount of thinning/smoothing to apply. We finally apply our proposed intensity estimation scheme to two datasets: locations of pine saplings (planar point pattern) and motor vehicle traffic accidents (linear network point pattern).

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arXiv2018

Prediction of spatial functional random processes: Comparing functional and spatio-temporal kriging approaches

In this paper, we present and compare functional and spatio-temporal (Sp.T.) kriging approaches to predict spatial functional random processes (which can also be viewed as Sp.T. random processes). Comparisons with respect to computational time and prediction performance via functional cross-validation is evaluated, mainly through a simulation study but also on two real data sets. We restrict comparisons to Sp.T. kriging versus ordinary kriging for functional data (OKFD), since the more flexible functional kriging approaches, pointwise functional kriging (PWFK) and functional kriging total model, coincide with OKFD in several situations. We contribute with new knowledge by proving that OKFD and PWFK coincide under certain conditions. From the simulation study, it is concluded that the prediction performance for the two kriging approaches in general is rather equal for stationary Sp.T. processes, with a tendency for functional kriging to work better for small sample sizes and Sp.T. kriging to work better for large sample sizes. For non-stationary Sp.T. processes, with a common deterministic time trend and/or time varying variances and dependence structure, OKFD performs better than Sp.T. kriging irrespective of sample size. For all simulated cases, the computational time for OKFD was considerably lower compared to those for the Sp.T. kriging methods.

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arXiv2017

Second-order and local characteristics of network intensity functions

The last decade has witnessed an increase of interest in the spatial analysis of structured point patterns over networks whose analysis is challenging because of geometrical complexities and unique methodological problems. In this context, it is essential to incorporate the network specificity into the analysis as the locations of events are restricted to areas covered by line segments. Relying on concepts originating from graph theory, we extend the notions of first-order network intensity functions to second-order and local network intensity functions. We consider two types of local indicators of network association functions which can be understood as adaptations of the primary ideas of local analysis on the plane. We develop the node-wise and cross-hierarchical type of local functions. A real dataset on urban disturbances is also presented.

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arXiv2017

Covariance Functions for Multivariate Gaussian Fields Evolving Temporally over Planet Earth

The construction of valid and flexible cross-covariance functions is a fundamental task for modeling multivariate space-time data arising from climatological and oceanographical phenomena. Indeed, a suitable specification of the covariance structure allows to capture both the space-time dependencies between the observations and the development of accurate predictions. For data observed over large portions of planet Earth it is necessary to take into account the curvature of the planet. Hence the need for random field models defined over spheres across time. In particular, the associated covariance function should depend on the geodesic distance, which is the most natural metric over the spherical surface. In this work, we propose a flexible parametric family of matrix-valued covariance functions, with both marginal and cross structure being of the Gneiting type. We additionally introduce a different multivariate Gneiting model based on the adaptation of the latent dimension approach to the spherical context. Finally, we assess the performance of our models through the study of a bivariate space-time data set of surface air temperatures and precipitations.

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arXiv2017

Substationarity in Spatial Point Processes

The goal of the article is to develop the approach of substationarity to spatial point processes (SPPs). Substationarity is a new concept, which has never been studied in the literature. It means that the distribution of SPPs can only be invariant under location shifts within a linear subspace of the domain. Theoretically, substationarity is a concept between stationariy and nonstationarity, but it belongs to nonstationarity. To formally propose the approach, the article provides the definition of substationarity and an estimation method for the first-order intensity function. As the linear subspace may be unknown, it recommends using a parametric way to estimate the linear subspace and a nonparametric way to estimate the first-order intensity function, indicating that it is a semiparametric approach. The simulation studies show that both the estimators of the linear subspace and the first-order intensity function are reliable. In an application to a forest wildfire data set, the article concludes that substationarity of wildfire occurrences may be assumed along the longitude, indicating that latitude is a more important factor than longitude in forest wildfire studies.

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arXiv2016

Graphical modelling of multivariate spatial point processes with continuous marks

This paper is the second in a series of papers which combine graphical modelling and marked spatial point patterns. Extending the previous results of \cite Eckardt (2016a), we introduce a marked spatial dependence graph model which depicts the global dependence structure of quantitatively marked multi-type points that occur in space based on the marked conditional partial spectral coherence. Most beneficial, no structural assumption with respect to the characteristics in the data are to be made prior to analysis. This approach presents a computationally efficient method of pattern recognition in highly structured and high dimensional multi-type spatial point processes where also quantitative marks are available. Unlike all previous methods, our new model permits the simultaneous analysis of all multivariate conditional interrelations. The new technique is illustrated analysing the diameter at breast hight of 37 different tree species recorded at 10053 locations in Duke Forest.

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arXiv2016

Structured network regression for spatial point patterns

The analysis of spatial point patterns that occur in the network domain have recently gained much attraction and various intensity functions and measures have been proposed. However, the linkage of spatial network statistics to regression models has not been approached so far. This paper presents a new regression approach which treats a generic intensity function of a planar point pattern that occurred on a network as the outcome of a set of different covariates and various graph statistics. Different to all alternative approaches, our model is the first which permits the statistical analysis of complex regression data in the context of network intensity functions for spatial point patterns. The potential of our new technique to model the structural dependencies of network intensity functions on various covariates and graph statistics is illustrated using call-in data on neighbour and community disturbances in an urban context.

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arXiv2016

Point patterns occurring on complex structures in space and space-time: An alternative network approach

This paper presents an alternative approach of analyzing possibly multitype point patterns in space and space-time that occur on network structures, and introduces several different graph-related intensity measures. The proposed formalism allows to control for processes on undirected, directional as well as partially directed network structures and is not restricted to linearity or circularity.

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arXiv2014

Spatio-temporal càdlàg functional marked point processes: Unifying spatio-temporal frameworks

This paper defines the class of càdlàg functional marked point processes (CFMPPs). These are (spatio-temporal) point processes marked by random elements which take values in a càdlàg function space, i.e. the marks are given by càdlàg stochastic processes. We generalise notions of marked (spatio-temporal) point processes and indicate how this class, in a sensible way, connects the point process framework with the random fields framework. We also show how they can be used to construct a class of spatio-temporal Boolean models, how to construct different classes of these models by choosing specific mark functions, and how càdlàg functional marked Cox processes have a double connection to random fields. We also discuss finite CFMPPs, purely temporally well-defined CFMPPs and Markov CFMPPs. Furthermore, we define characteristics such as product densities, Palm distributions and conditional intensities, in order to develop statistical inference tools such as likelihood estimation schemes.

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arXiv2008

The Dagum family of isotropic correlation functions

A function $ρ:[0,\infty)\to(0,1]$ is a completely monotonic function if and only if $ρ(\Vert\mathbf{x}\Vert^2)$ is positive definite on $\mathbb{R}^d$ for all $d$ and thus it represents the correlation function of a weakly stationary and isotropic Gaussian random field. Radial positive definite functions are also of importance as they represent characteristic functions of spherically symmetric probability distributions. In this paper, we analyze the function \[ρ(β,γ)(x)=1-\biggl(\frac{x^β}{1+x^β}\biggr )^γ,\qquad x\ge 0, β,γ>0,\] called the Dagum function, and show those ranges for which this function is completely monotonic, that is, positive definite, on any $d$-dimensional Euclidean space. Important relations arise with other families of completely monotonic and logarithmically completely monotonic functions.

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arXiv2005

Detection of cosmic filaments using the Candy model

We propose to apply a marked point process to automatically delineate filaments of the large-scale structure in redshift catalogues. We illustrate the feasibility of the idea on an example of simulated catalogues, describe the procedure, and characterize the results. We find the distribution of the length of the filaments, and suggest how to use this approach to obtain other statistical characteristics of filamentary networks.

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