Discussion of ‘Marked Spatial Point Processes: Current State and Extensions to Point Processes on Linear Networks’ by Matthias Eckardt and Mehdi Moradi

We congratulate Professors Eckardt and Moradi on their fine paper in which they survey the state of the art of summary statistics for marked point processes. The authors focus on non-stationary point processes and distinguish between discrete, real-valued and objectvalued marks. The case of point processes in an Euclidean space with discrete marks is by far the most well studied. Here, centre stage is taken by the cross K, H and J statistics. After a brief detour into the frequency domain, the authors consider point processes on linear networks. The concept of intensity-reweighted moment pseudo-stationarity (IRMPS) is introduced and used to define counterparts of the cross statistics just mentioned.