This article proposes log-linear models for the latent intensity functions of replicated spatio-temporal point processes. By simultaneously fitting correlated spatial and temporal Karhunen–Loève expansions, these models produce spatial and temporal components that are usually easy to interpret and capture the main directions of spatio-temporal correlation. The asymptotic distribution of the estimators is derived, and their finite sample properties are studied by simulation. As an example of application, we analyze the spatio-temporal patterns of usage of a bike station in the Divvy bike-sharing system of the city of Chicago.

中文翻译：

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复制点过程时空协变的双随机模型

本文提出了复制时空点过程的潜在强度函数的对数线性模型。通过同时拟合相关的空间和时间 Karhunen-Loève 展开，这些模型产生通常易于解释和捕捉时空相关性的主要方向的空间和时间分量。推导了估计量的渐近分布，并通过仿真研究了它们的有限样本性质。作为应用示例，我们分析了芝加哥市 Divvy 自行车共享系统中自行车站的时空使用模式。