Detecting Dependence Between Marks and Locations of Marked Point Processes

Abstract

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.

Improving the Integration of Coppice Forest Protection in Rockfall Model

“…Pour les deux équations, les e ets de bords sont corrigés par la méthode proposée par [Ripley, 1977] et décrite dans [Goreaud and Pélissier, 2003,Schlather et al, 2004,Wiegand and A. Moloney, 2004.…”

Random Marked Sets

“…For the particular case of marked point processes, several tests for the random field model hypothesis have been developed [11], [24]. Example 2.…”

Assessing the effect of clustered and biased multi‐stage sampling

“…In a context of marked point processes, Schlather et al (2004) investigate marks and locations interactions, by introducing functions of the inter-point distance u, under the assumption of stationary and isotropy. One of these functions denotes the conditional expectation of a mark, given that there is a further point of the process a distance u away.…”

“…maximum values search). Schlather et al (2004) propose methods to detect the dependence between marks and locations of marked point processes. As described in Mateu and Ribeiro (1999), the random field and the marked point process are two type of spatial processes such that:…”

“…Example of references concerned with this subject are Walder and Stoyan (1996) and Schlather (2002). Schlather et al (2004) indicate next two likely situations for point and data processes being dependent and subsequent failure of this important geostatistics assumption. Firstly, if the dependency is an intrinsic property of the data themselves, for example the relative positions of trees impact on their size due to their competition for light and nutrient.…”