Conditionally heteroscedastic intensity‐dependent marking of log Gaussian Cox processes

Abstract

Spatial marked point processes are models for systems of points which are randomly distributed in space and provided with measured quantities called marks. This study deals with marking, that is methods of constructing marked point processes from unmarked ones. The focus is density‐dependent marking where the local point intensity affects the mark distribution. This study develops new markings for log Gaussian Cox processes. In these markings, both the mean and variance of the mark distribution depend on the local intensity. The mean, variance and mark correlation properties are presented for the new markings, and a Bayesian estimation procedure is suggested for statistical inference. The performance of the new approach is studied by means of simulation experiments. As an example, a tropical rainforest data is modelled.