Function-valued marked spatial point processes on linear networks: application to urban cycling profiles

TL;DR

This paper develops new methods for analyzing function-valued marked spatial point processes on linear networks, with applications to urban cycling profiles, enhancing understanding of spatial dependence and dispersion.

Contribution

It introduces novel marked summary characteristics for function-valued marks on linear networks, with validation through simulation and real-world urban cycling data analysis.

Findings

Marked summary characteristics effectively capture spatial dependence.

Simulation confirms robustness of proposed methods.

Application reveals spatial patterns in urban cycling profiles.

Abstract

In the literature on spatial point processes, there is an emerging challenge in studying marked point processes with points being labelled by functions. In this paper, we focus on point processes living on linear networks and, from distinct points of view, propose several marked summary characteristics that are of great use in studying the average association and dispersion of the function-valued marks. Through a simulation study, we evaluate the performance of our proposed marked summary characteristics, both when marks are independent and when some sort of spatial dependence is evident among them. Finally, we employ our proposed mark summary characteristics to study the spatial structure of urban cycling profiles in Vancouver, Canada.