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Structured space-sphere point processes and $K$-functions by Møller, Jesper; Christensen, Heidi S.; Cuevas-Pacheco, Francisco; Christoffersen, Andreas D. is a scholarly article available to read on EtoBox.

What is Structured space-sphere point processes and $K$-functions about?

This paper concerns space-sphere point processes, that is, point processes on the product space of $\mathbb R^d$ (the $d$-dimensional Euclidean space) and $\mathbb S^k$ (the $k$-dimen\-sional 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 $\mathbb R^d$ 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 $k$.

Author

Møller, Jesper; Christensen, Heidi S.; Cuevas-Pacheco, Francisco; Christoffersen, Andreas D.

Published

2018

Language

EN