Structured Space-Sphere Point Processes and K-Functions

Jesper Møller (), Heidi S. Christensen (), Francisco Cuevas-Pacheco () and Andreas D. Christoffersen ()
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Jesper Møller: Aalborg University
Heidi S. Christensen: Aalborg University
Francisco Cuevas-Pacheco: Aalborg University
Andreas D. Christoffersen: Aalborg University

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 2, 569-591

Abstract: Abstract This paper concerns space-sphere point processes, that is, point processes on the product space of ℝ d $\mathbb {R}^{d}$ (the d-dimensional Euclidean space) and S k $\mathbb {S}^{k}$ (the k-dimensional sphere). We consider specific classes of models for space-sphere point processes, which are adaptations of existing models for either spherical or spatial point processes. For model checking or fitting, we present the space-sphere K-function which is a natural extension of the inhomogeneous K-function for point processes on ℝ d $\mathbb {R}^{d}$ to the case of space-sphere point processes. Under the assumption that the intensity and pair correlation function both have a certain separable structure, the space-sphere K-function is shown to be proportional to the product of the inhomogeneous spatial and spherical K-functions. For the presented space-sphere point process models, we discuss cases where such a separable structure can be obtained. The usefulness of the space-sphere K-function is illustrated for real and simulated datasets with varying dimensions d and k.

Keywords: First and second order separability; Functional summary statistic; Log Gaussian Cox process; Pair correlation function; Shot noise Cox process; 60G55; 62M30 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11009-019-09712-w

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