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.

翻译：摘要：本文通过两项相互关联的贡献，将空间点过程的统计推断与等待中行人人群的分析联系起来。首先，在方法论层面，我们开发了一种针对半参数空间点过程模型的推断程序，利用重复的空间模式（即来自同一过程的多个近似独立的实现）。其次，我们证明了空间点过程为等待行人提供了合适的建模框架，捕捉了两个关键方面：由地点吸引力驱动的空间非均匀性和行人之间的排斥性相互作用。这两个组成部分本身对推断问题至关重要，因为空间点过程建模的关键在于将背景强度与相互作用分离开来。尽管重复空间模式在点过程文献中较为罕见，但通过一个独特的真实行人数据集，我们在此处获得了此类数据，从而将方法论发展与实际应用直接联系起来。我们使用所提出的方法，在模拟研究和实际案例研究中拟合并评估了行列式点过程与吉布斯点过程。尽管在分离非均匀性与相互作用的影响方面仍存在持续挑战，这些模型能够重现等待行人的关键经验特征。