  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.
