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

TL;DR

This paper reviews and introduces new Cox process models on linear networks driven by transformed Gaussian processes, including statistical procedures, simulation algorithms, and metric considerations for these models.

Contribution

It introduces three novel classes of Cox processes on linear networks and develops statistical methods and simulation algorithms for these models.

Findings

New Cox process models on linear networks are proposed.

Statistical procedures for these models are developed.

Simulation algorithms and metric discussions are provided.

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.