In the first part of the talk we will investigate differences between a space-time separable model and an ambit model in the context of shot-noise Cox processes with continuous time. The criteria are derived from second-order properties. In the second part of the talk a discrete time model of a planar union of interacting discs given by a probability density with respect to a Poisson process of discs is considered. The state vector and auxiliary parameters are estimated using sequential Monte Carlo methods. The estimation properties are compared in a simulation study.
This lecture makes use of student's work of Antonín Koubek and Markéta Zikmundová from Charles University under my supervision.