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 K-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.