Point processes on linear networks are increasingly being considered to analyse events occurring on particular network-based structures. In this paper, we extend Local Indicators of Spatio-Temporal Association (LISTA) functions to the non-Euclidean space of linear networks, allowing to obtain information on how events relate to nearby events. In particular, we propose the local version of two inhomogeneous second-order statistics for spatio-temporal point processes on linear networks, the K- and the pair correlation functions. We put particular emphasis on the local K-functions, deriving come theoretical results which enable us to show that these LISTA functions are useful for diagnostics of models specified on networks, and can be helpful to assess the goodness-of-fit of different spatio-temporal models fitted to point patterns occurring on linear networks. Our methods do not rely on any particular model assumption on the data, and thus they can be applied for whatever is the underlying model of the process. We finally present a real data analysis of traffic accidents in Medellin (Colombia).

越来越多地考虑线性网络上的点过程来分析发生在特定网络结构上的事件。在本文中，我们将时空关联的局部指标 (LISTA) 函数扩展到线性网络的非欧几里得空间，从而获得有关事件如何与附近事件相关的信息。特别是，我们提出了线性网络上时空点过程的两个非齐次二阶统计的本地版本，K - 和对相关函数。我们特别强调本地K-函数，得出的理论结果使我们能够证明这些 LISTA 函数对于网络上指定的模型的诊断很有用，并且有助于评估拟合到点模式的不同时空模型的拟合优度。线性网络。我们的方法不依赖于对数据的任何特定模型假设，因此它们可以应用于任何过程的基础模型。我们最终展示了麦德林（哥伦比亚）交通事故的真实数据分析。