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There is a lack of point process models on linear networks. For an arbitrarylinear network, we consider new models for a Cox process with an isotropic paircorrelation function obtained in various ways by transforming an isotropicGaussian process which is used for driving the random intensity function of theCox process. In particular we introduce three model classes given by logGaussian, interrupted, and permanental Cox processes on linear networks, andconsider for the first time statistical procedures and applications forparametric families of such models. Moreover, we construct new simulationalgorithms for Gaussian processes on linear networks and discuss whether thegeodesic metric or the resistance metric should be used for the kind of Coxprocesses studied in this paper.

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