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

TL;DR

This paper introduces new statistical methods for analyzing spatial point processes with graph-valued marks, addressing a gap in existing techniques for complex relational data, motivated by nerve fiber data analysis.

Contribution

It develops novel mark summary characteristics for graph-valued marks in spatial point processes, enabling analysis of relational structures within complex event data.

Findings

New graph-valued mark summary characteristics introduced

Applied methods to epidermal nerve fiber data

Demonstrated effectiveness in capturing relational structures

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.