Discussion of the Paper “Marked Spatial Point Processes: Current State and Extensions to Point Processes on Linear Networks”

The authors of the paper under discussion have done an excellent job in providing a summary of the current state of a large part of the field, as well as proposing extensions to marked linear network point processes.Both are welcomed additions to the literature, and we believe that the paper will be a valuable resource for the spatial statistics community.The title of the paper might give the impression that the paper is a review of "all of (statistics for)" marked point processes, which in itself would have been quite an endeavour to complete, given the long history of the field.Fortunately, the authors restrict themselves to reviewing summary statistics for point processes, which is more manageable, given the page limitation.For the reader who anticipates a full review of statistics for marked point processes, we would, however, like to highlight a few important parts of the field.It should be noted that this list is far from complete in terms of additional topics.• Marked temporal point processes, e.g.Hawkes and ETAS processes, which are expressed through temporal conditional intensity functions, have a long history and have the advantage that the likelihood function is known in closed form (Daley and Vere-Jones 2003, 2008).This, in turn, leads to a statistical analysis much in line with classical statistics.A fairly recent review on the topic can be found in Reinhart (2018).• There is a long trajectory of papers dealing with the Growth-Interaction process of