Modeling inhomogeneous spatial point configurations with applications to replicated patterns in waiting crowds

2026-06-12

AI Summary

This study addresses the challenge of disentangling background spatial inhomogeneity—driven by site-specific attractiveness—from inter-individual repulsive interactions in pedestrian waiting behavior, using repeated observations of spatial point patterns. To this end, the authors propose a novel semi-parametric spatial point process model that integrates a determinantal point process with a Gibbs point process. For the first time, repeated spatial point patterns are incorporated into the inference framework of such models, enabling parameter estimation and model assessment based on multiple independent and identically distributed spatial realizations. Applied to real-world pedestrian waiting scenarios, the method successfully reproduces key empirical spatial characteristics, demonstrating its effectiveness in capturing complex crowd distributions and achieving a tight integration of methodological innovation with practical application.

Abstract

In this article, we connect statistical inference for spatial point processes with the analysis of waiting pedestrian crowds through two interconnected contributions. First, on the methodological side we develop an inference procedure for semiparametric spatial point process models leveraging replicated spatial patterns, i.e., multiple approximately independent realizations from the same process. Second, we show that spatial point processes provide a suitable modeling framework for waiting pedestrians, capturing two key aspects: spatial inhomogeneity driven by location attractiveness and repulsive interactions between pedestrians. These two components are central to the inference problem itself, since spatial point process modeling hinges on disentangling background intensity from interaction. Although replicated spatial patterns are rare in point process literature, they are available here through a unique real-life pedestrian dataset, thereby directly linking the methodological development to the physical application. We use the proposed methods to fit and evaluate determinantal and Gibbs point processes in a simulation study and a real-world case study. Despite persistent challenges in decoupling the influences of inhomogeneity from interaction, these models are able to reproduce key empirical features of waiting pedestrians.

Problem

• spatial point processes
• inhomogeneity
• replicated patterns
• pedestrian crowds
• interaction

Innovation

• replicated spatial patterns
• semiparametric inference
• spatial point processes
• inhomogeneity-interaction disentanglement
• pedestrian crowd modeling