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Spatial Poisson point processes on finite-dimensional Euclidean space provide fundamental mathematical tools for modeling random spatial point patterns. In this paper, we introduce and analyze several Poisson-type spatial point processes.…

The fundamental functional summary statistics used for studying spatial point patterns are developed for marked homogeneous and inhomogeneous point processes on the surface of a sphere. These are extended to point processes on the surface…

U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…

This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…

Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…

Aggregation patterns are often visually detected in sets of location data. These clusters may be the result of interesting dynamics or the effect of pure randomness. We build an asymptotically Gaussian test for the hypothesis of randomness…

The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint…

First-order separability of a spatio-temporal point process plays a fundamental role in the analysis of spatio-temporal point pattern data. While it is often a convenient assumption that simplifies the analysis greatly, existing…

Random point patterns are ubiquitous in nature, and statistical models such as point processes, i.e., algorithms that generate stochastic collections of points, are commonly used to simulate and interpret them. We propose an application of…

We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the `space' being of a general economic or social nature. Dependence can be parametric, parametric with increasing…

In this paper we address the statistical problem of testing if a stationary process is Gaussian. The observation consists in a finite sample path of the process. Using a random projection technique introduced and studied in Cuesta-Albertos…

In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…

The point process of vertices of an iteration infinitely divisible or more specifically of an iteration stable random tessellation in the Euclidean plane is considered. We explicitly determine its covariance measure and its pair-correlation…

Spatial point processes are used as models in many different fields ranging from ecology and forestry to cosmology and materials science. In recent years, model validation, and in particular goodness-of-fit testing of a proposed point…

In many contexts such as queuing theory, spatial statistics, geostatistics and meteorology, data are observed at irregular spatial positions. One model of this situation involves considering the observation points as generated by a Poisson…

Point processes have broad applications in science and engineering. In physics, their use ranges from quantum chaos to statistical mechanics of many-particle systems. We introduce a spatial form factor (SFF) for the characterization of…

The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision and beyond. While many statistical frameworks have been developed for the classification problem, most are strongly tied to…

In this paper we introduce a method which allows us to study properties of the random uniform simplicial complex. That is, we assign equal probability to all simplicial complexes with a given number of vertices and then consider properties…

In this paper, we propose a new comparison tool for spatial homogeneity of point processes, based on the joint examination of void probabilities and factorial moment measures. We prove that determinantal and permanental processes, as well…

Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function…