Discussion of the Paper by Eckardt and Moradi

I appreciate the editor's invitation to discuss Eckardt and Moradi's paper and to delve into the statistics of marked point processes, a field of spatial statistics in which I have been engaged for years.Although I am not as active in this field as I used to be and may not be aware of its latest developments, I will approach this discussion as an experienced user of the relevant statistical methods.My tendency is to question the 'why' when analyzing data.A crucial inquiry in utilizing statistics for marked point processes is determining how the marks or marked points were generated and which models can be employed to comprehend this process.The paper lacks a thorough discussion of this issue.As we are all aware, the simplest scenario is independent marking, which the authors use as a null model.A more complex model is the random field model, where the marks come from an independent random field and are therefore spatially correlated.Maybe it could be an improved null model for the second example with the street trees.Even this simple model is not considered by the authors.Are there really no other interesting modern models for marked point processes?I noticed the idea of labeling the protein points with the values of their local intensity.This reminds me of a model considered in Wälder and Stoyan (1997), where, for a homogeneous Poisson point process, the number of points in a circle around a point x was used as its mark m(x).Of course, it is not at all surprising that for intensity marking the function κ mm (r ), as used by the authors, takes large values (for small r ), since in intensity marking large marks appear where the points are dense and close together.Equation ( 12) with the definition of κ t f (r ) caught my interest.Why is there a κ?The books of Baddeley et al. (2015), Illian et al. (2008) and Wiegand and Moloney (2014) use k instead.Why this change that might confuse beginners?I had a look at old papers and found a κ(r ) in Stoyan (1984) for the non-normalized version of k mm (r ).However, already in Penttinen and Stoyan (1989) there is then the usual notation with k f (r ).By the way, I would rewrite equation ( 12) as