Graphical modelling of multivariate spatial point processes with continuous marks

Abstract: This paper is the second in a series of papers which combine graphical modelling and marked spatial point patterns. Extending the previous results of \cite Eckardt (2016a), we introduce a marked spatial dependence graph model which depicts the global dependence structure of quantitatively marked multi-type points that occur in space based on the marked conditional partial spectral coherence. Most beneficial, no structural assumption with respect to the characteristics in the data are to be made prior to analysis. This approach presents a computationally efficient method of pattern recognition in highly structured and high dimensional multi-type spatial point processes where also quantitative marks are available. Unlike all previous methods, our new model permits the simultaneous analysis of all multivariate conditional interrelations. The new technique is illustrated analysing the diameter at breast hight of 37 different tree species recorded at 10053 locations in Duke Forest.