The emergence of distinct local mark behaviours is becoming increasingly common in the applications of spatial marked point processes. This dynamic highlights the limitations of existing global mark correlation functions in accurately identifying the true patterns of mark associations/variations among points as distinct mark behaviours might dominate one another, giving rise to an incomplete understanding of mark associations. In this paper, we introduce a family of local indicators of mark association (LIMA) functions for spatial marked point processes. These functions are defined on general state spaces and can include marks that are either real-valued or function-valued. Unlike global mark correlation functions, which are often distorted by the existence of distinct mark behaviours, LIMA functions reliably identify all types of mark associations and variations among points. Additionally, they accurately determine the interpoint distances where individual points show significant mark associations. Through simulation studies, featuring various scenarios, and four real applications in forestry, criminology, and urban mobility, we study spatial marked point processes in $\R^2$ and on linear networks with either real-valued or function-valued marks, demonstrating that LIMA functions significantly outperform the existing global mark correlation functions.

翻译：在空间标记点过程的应用中，局部标记行为的差异性日益普遍。这一动态凸显出现有全局标记相关函数在准确识别点之间真实标记关联/变异模式方面的局限性，因为不同的标记行为可能相互主导，导致对标记关联的理解不完整。本文针对空间标记点过程引入了一族局部标记关联指标（LIMA）函数。这些函数定义在一般状态空间上，可包含实值或函数值的标记。与常因不同标记行为存在而失真的全局标记相关函数不同，LIMA函数能可靠识别所有类型的点间标记关联与变异。此外，它们能精确确定单个点呈现显著标记关联的点间距离。通过包含多种情景的模拟研究，以及在林业、犯罪学和城市交通领域的四个实际应用，我们研究了$\R^2$空间和线性网络上具有实值或函数值标记的空间标记点过程，证明LIMA函数显著优于现有的全局标记相关函数。