Within the applications of spatial point processes, it is increasingly becoming common that events are labeled by marks, prompting an exploration beyond the spatial distribution of events by incorporating the marks in the undertaken analysis. In this paper, we first consider marked spatial point processes in $\R^2$, where marks are either integer-valued, real-valued, or object-valued, and review the state-of-the-art to analyze the spatial structure and type of interaction/correlation between marks. More specifically, we review cross/dot-type summary characteristics, mark-weighted summary characteristics, various mark correlation functions, and frequency domain approaches. Second, we propose novel cross/dot-type higher-order summary characteristics, mark-weighted summary characteristics, and mark correlation functions for marked point processes on linear networks. Through a simulation study, we show that ignoring the underlying network gives rise to erroneous conclusions about the interaction/correlation between marks. Finally, we consider two applications: the locations of two types of butterflies in Melbourne, Australia, and the locations of public trees along the street network of Vancouver, Canada, where trees are labeled by their diameters at breast height.

翻译：在空间点过程的应用中，事件被标记所标注的情况日益普遍，这促使我们在分析中引入标记，以超越仅关注事件空间分布的范畴。本文首先考虑 $\R^2$ 中标记为整数值、实数值或对象值的带标记空间点过程，并回顾分析标记间空间结构与交互/相关类型的前沿方法。具体而言，我们综述了交叉/点型汇总特征、标记加权汇总特征、各种标记相关函数以及频域方法。其次，针对线性网络上的带标记点过程，我们提出了新型交叉/点型高阶汇总特征、标记加权汇总特征及标记相关函数。通过模拟研究，我们表明忽略底层网络会导致关于标记间交互/相关性的错误结论。最后，我们考虑两个实际应用：澳大利亚墨尔本两种蝴蝶的分布位置，以及加拿大温哥华街道网络中公共树木的位置（这些树木以胸径为标记）。