Pseudo-likelihood approach for pair potential estimation of Gibbs processes - Särkkä, Aila (1993)
This work concentrates on pair potential estimation of unmarked and marked Gibbs point processes through the pseudo-likelihood method. The estimation equations are derived for discretely and continuously marked Gibbs processes on bounded subsets of Rd and applied to the analysis of three empirical data. This experimentation shows that the pseudo-likelihood method can fail: it leads to overestimation probably because of strong interactions between the objects. The method appears to be sensitive to outlying orservations. Several techniques to detect outlying observations are suggested and bias corrections are discussed. Connection between the pseudo-likelihood and the Takacs-Fiksel estimation methods is shown for marked point processes with a general pair potential function. As a consequence, it is proved that the pseudo-likelihood method can be applied also to modelling data collected through field measurements. As an application to practical forestry, interactions between trees in pine and spruce forests in Central Finland are studied using data consisting of so-called INKA sample plots collected by The Finnish Forest Research Institute.