Detecting dependence between marks and locations of marked point processes

Two characteristics for stationary and isotropic marked point processes, E(r)and V(r), are introduced that allow for investigating mark-point interactions. These quantities are functions of the inter-point distance rand denote the conditional expectation and the conditional variance of a mark, respectively, given there is a further point of the process a distance rapart. Tests based on Eand Vare presented that help to decide whether the values of the marks can be modelled by random field that is independent of the unmarked point process. We demonstrate the use of our approach for three data sets in forestry