This paper contributes to the multivariate analysis of marked spatio-temporal point process data by introducing different partial point characteristics and extending the spatial dependence graph model formalism. Our approach yields a unified framework for different types of spatio-temporal data including both, purely qualitatively (multivariate) cases and multivariate cases with additional quantitative marks. The proposed graphical model is defined through partial spectral density characteristics, it is highly computationally efficient and reflects the conditional similarity among sets of spatio-temporal sub-processes of either points or marked points with identical discrete marks. The paper considers three applications, two on crime data and a third one on forestry.

中文翻译：

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多类型和多变量标记时空点过程的图形建模和局部特征

本文通过引入不同的局部点特征和扩展空间依赖图模型形式，为标记时空点过程数据的多元分析做出贡献。我们的方法为不同类型的时空数据生成了一个统一的框架，包括纯定性（多变量）案例和带有额外定量标记的多变量案例。所提出的图形模型是通过部分谱密度特征定义的，它具有很高的计算效率，并反映了点或具有相同离散标记的标记点的时空子过程集之间的条件相似性。该论文考虑了三个应用，两个关于犯罪数据，第三个关于林业。