Cox processes driven by transformed Gaussian processes on linear networks -- A review and new contributions

2022/12/16 by Jesper Møller, Jakob Gulddahl Rasmussen, Møller, Jesper +1 · 1 citation
Mathematics · #FOS: Mathematics #Morphological variations and asymmetry #Point processes and geometric inequalities #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2212.08402

openalex publication_date 2022/12/16 · openalex created_date 2023/01/03 · openalex updated_date 2026/07/28

Abstract

There is a lack of point process models on linear networks. For an arbitrary linear network, we consider new models for a Cox process with an isotropic pair correlation function obtained in various ways by transforming an isotropic Gaussian process which is used for driving the random intensity function of the Cox process. In particular we introduce three model classes given by log Gaussian, interrupted, and permanental Cox processes on linear networks, and consider for the first time statistical procedures and applications for parametric families of such models. Moreover, we construct new simulation algorithms for Gaussian processes on linear networks and discuss whether the geodesic metric or the resistance metric should be used for the kind of Cox processes studied in this paper.

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