Detecting dependence between marks and locations of marked point processes

We introduce two characteristics for stationary and isotropic marked point proces- ses, "E"("h") and "V"("h"), and describe their use in investigating mark-point interactions. These quantities are functions of the interpoint distance "h" and denote the conditional expectation and the conditional variance of a mark respectively, given that there is a further point of the process a distance "h" away. We present tests based on "E" and "V" for the hypothesis that the values of the marks can be modelled by a random field which is independent of the unmarked point process. We apply the methods to two data sets in forestry. Copyright 2004 Royal Statistical Society.