First- and Second-Order Characteristics of Spatio-Temporal Point Processes on Linear Networks

We present several characteristics for spatio-temporal point patterns when the spatial locations are restricted to a linear network. A nonparametric kernel-based intensity estimator is proposed to highlight the concentration of events within the network and time, either jointly or separately. We also provide second-order characteristics for spatio-temporal point patterns on linear networks such as <i>K</i>-function and pair correlation function to analyze the type of interaction between points. They are independent of network’s geometry and have known values for Poisson point processes. Finally, we consider some applications to traffic accidents and demonstrate our findings by analyzing datasets of Houston (United States), Medellín (Colombia), and Eastbourne (United Kingdom). Supplementary materials for this article are available online.

针对空间位置受限在线性网络（linear network）上的时空点模式（spatio-temporal point patterns），本文提出了若干特征描述指标。本文提出一种基于非参数核的强度估计器，可单独或联合刻画事件在网络空间与时间维度上的聚集程度。此外，本文还针对线性网络上的时空点模式给出了二阶特征指标，包括K函数（K-function）与对相关函数（pair correlation function），用于分析点之间的相互作用类型。该类指标不受网络几何结构的影响，且在泊松点过程（Poisson point process）下具有已知的理论取值。最后，本文将所提方法应用于交通事故分析场景，并通过分析美国休斯顿、哥伦比亚麦德林以及英国伊斯特本的数据集验证了研究结论的有效性。本文的补充材料可在线获取。