Parameter estimation for growth interaction processes using spatio-temporal information

Methods for the parameter estimation for a spatio-temporal marked point process model, the so-called growth-interaction model, are investigated. Least squares estimation methods for this model found in the literature are only concerned with fitting the mark distribution observed in the data. These methods are unable to distinguish between models which have the same birth, death, interaction and growth functions and parameters but different arrival strategies for the points. Hence, they are extended such that the spatial structure of a point pattern is also taken into account. The suggested methods are evaluated in a simulation study and applied to a small data set from forestry.