Spatio-temporal areal data can be seen as a collection of time series which are spatially correlated, according to a specific neighbouring structure. Motivated by a dataset on mobile phone usage in the Metropolitan area of Milan, Italy, we propose a semi-parametric hierarchical Bayesian model allowing for time-varying as well as spatial model-based clustering. Our approach incorporates the notion of regimes that describe changing patterns over work and night hours as well as weekdays/weekends. Changes across regimes are considered by means of temporal changepoint components that allow for different hierarchical structures specified across time points. The changepoints might occur within fixed time windows over the day. The model features a novel random partition prior that incorporates the desired spatial features and encourages co-clustering based on areal proximity. We explore properties of the model by way of extensive simulation studies from which we collect valuable information. Finally, we discuss the application to the motivating data, where the main goal is to spatially cluster population patterns of mobile phone usage.

翻译：时空面域数据可视为根据特定邻接结构存在空间相关性的时间序列集合。受意大利米兰大都会区手机使用数据集的驱动，我们提出了一种半参数层次贝叶斯模型，该模型允许进行时变及基于模型的空间聚类。我们的方法融合了"状态（regime）"概念，用以描述工作日/周末及工作时间/夜间时段的变化模式。通过引入时变变点成分来实现状态间的转变，该成分允许在不同时间点上指定不同的层次结构，且变点可能发生在一天中的固定时间窗内。该模型采用一种新颖的随机分区先验，该先验整合了期望的空间特征，并基于面域邻近性促进协同聚类。通过广泛的模拟研究，我们探索了模型性质并获得了宝贵信息。最后，我们讨论了该模型在原始数据集上的应用，其核心目标是对手机使用人口模式进行空间聚类。