Local Indicators of Mark Association for Marked Spatial Point Processes

Distinct local mark behaviours are increasingly observed in applications of marked spatial point processes. These local differences reveal important limitations of global mark correlation functions, which can fail to identify true mark associations when some mark behaviours dominate others. In this paper, we introduce a family of local indicators of mark association (LIMA) for marked spatial point processes. These functions are defined for point processes on general state spaces and accommodate both real-valued and object-valued marks. Unlike global mark correlation functions, which can be distorted when distinct mark behaviours coexist, LIMA functions reliably identify all types of mark associations among points. Moreover, they identify the interpoint distances at which individual points exhibit significant mark associations. Through a range of simulated scenarios and two forestry applications involving real- and function-valued marks, we demonstrate the performance of LIMA functions. In particular, LIMA functions substantially outperform existing global mark correlation functions in detecting mark associations, quantifying their variation, and identifying their effective spatial range.