Adjusting for Social Groups in Spatial Point Process Models for Waiting Pedestrian Configurations
Abstract
The spatial distribution of waiting pedestrians has two primary drivers: environmental preference and interaction with other pedestrians. Spatial point processes naturally capture both spatial heterogeneity and repulsive interaction. In previous work (Sickert Karam et al., arXiv:2606.14532, 2026), we proposed a Gibbs model with inhomogeneous intensity and a modified Diggle-Gates-Stibbard interaction function, which reproduces many phenomena in replicated patterns of pedestrians waiting at a train station. Its single interaction function acts as an effective interaction, averaging over behavioral regimes such as interactions within social groups and among strangers. In this article, we show how groups affect distance-based summary statistics and take first steps towards accounting for them. We detect groups from pairwise distances and contact durations, replace each group by a ``macro-pedestrian'' at its average position, and refit the model. This yields a larger interaction range and better agreement in nearest-neighbor statistics than the original model, although the two fits concern different datasets and centroid-based distances likely overstate repulsion. This first attempt thus resolves some discrepancies but falls short of a fully adequate solution, opening avenues for further research.
Related
- Modeling inhomogeneous spatial point configurations with applications to replicated patterns in real-life waiting crowds
- A new class of pyramidal central configurations for spatial Newtonian 6-body problems
- A zero-inflated mixed-effects spatial point process for grouped storm loss data
- Divide-and-Conquer Neural Bayes Estimation for Spatial and Spatiotemporal Point Process Models
- Temporal Fourier Likelihoods with Spatial Hilbert-Space Gaussian Process Approximations
BibTeX
@misc{karam2026adjusting,
title = {{Adjusting for Social Groups in Spatial Point Process Models for Waiting Pedestrian Configurations}},
author = {Lars Sickert Karam and Rui M. Castro and Maarten Schoukens and Alessandro Corbetta},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09883},
eprint = {2610.09883},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09883},
}
RIS
TY - UNPB
TI - Adjusting for Social Groups in Spatial Point Process Models for Waiting Pedestrian Configurations
AU - Lars Sickert Karam
AU - Rui M. Castro
AU - Maarten Schoukens
AU - Alessandro Corbetta
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09883
UR - https://arxiv.org/abs/2610.09883
AB - The spatial distribution of waiting pedestrians has two primary drivers: environmental preference and interaction with other pedestrians. Spatial point processes naturally capture both spatial heterogeneity and repulsive interaction. In previous work (Sickert Karam et al., arXiv:2606.14532, 2026), we proposed a Gibbs model with inhomogeneous intensity and a modified Diggle-Gates-Stibbard interaction function, which reproduces many phenomena in replicated patterns of pedestrians waiting at a train station. Its single interaction function acts as an effective interaction, averaging over behavioral regimes such as interactions within social groups and among strangers. In this article, we show how groups affect distance-based summary statistics and take first steps towards accounting for them. We detect groups from pairwise distances and contact durations, replace each group by a ``macro-pedestrian'' at its average position, and refit the model. This yields a larger interaction range and better agreement in nearest-neighbor statistics than the original model, although the two fits concern different datasets and centroid-based distances likely overstate repulsion. This first attempt thus resolves some discrepancies but falls short of a fully adequate solution, opening avenues for further research.
ER -