Second-order characteristics for spatial point processes with graph-valued marks

Abstract: The immense progress in data collection and storage capacities have yielded rather complex, challenging spatial event-type data, where each event location is augmented by a non-simple mark. Despite the growing interest in analysing such complex event patterns, the methodology for such analysis is not embedded well in the literature. In particular, the literature lacks statistical methods to analyse marks which are characterised by an inherent relational structure, i.e.\ where the mark is graph-valued. Motivated by epidermal nerve fibre data, we introduce different mark summary characteristics, which investigate the average variation or association between pairs of graph-valued marks, and apply some of the methods to the nerve data.