Paper "Inhomogeneous mark correlation functions for general marked point processes" by Moradi and Eckardt accepeted by Biometrics
The paper Inhomogeneous mark correlation functions for general marked point processes by Moradi M. and Eckardt M. is accepted by Biometrics.
Abstract:
Spatial phenomena in environmental and biological contexts often involve events that are unevenly distributed across space and carry attributes whose associations or variations depend on location.
In this paper, we introduce a class of inhomogeneous mark correlation functions that capture mark associations and variations while explicitly accounting for spatial inhomogeneity in the underlying events. The proposed functions are designed to quantify how, on average, marks vary or associate with one another as a function of pairwise spatial distance.
We develop nonparametric estimators for these functions and evaluate their performance through simulation studies covering a range of scenarios involving mark association or variation. These scenarios span from nonstationary point patterns without spatial interaction to patterns characterised by clustering tendencies.
Our simulations reveal the shortcomings of traditional methods when spatial inhomogeneity is present, underscoring the necessity of the proposed approach. The results further demonstrate that our estimators accurately identify both the sign (positive or negative) and the effective spatial range of detected mark associations or variations.
Finally, we apply the inhomogeneous mark correlation functions to two distinct forest ecosystems: Longleaf pine trees in southern Georgia, USA, marked by diameter at breast height, and Scots pine trees in Pfynwald, Switzerland, marked by tree height. Our findings show that the proposed methods provide deeper and more detailed insights into tree growth patterns than traditional approaches.