Sequential Spatial Point Process Models for Spatio-Temporal Point Processes: A Self-Interactive Model with Application to Forest Tree Data

Abstract: We model the spatial dynamics of a forest stand by using a special class of spatio-temporal point processes, the sequential spatial point process, where the spatial dimension is parameterized and the time component is atomic. The sequential spatial point processes differ from spatial point processes in the sense that the realizations are ordered sequences of spatial locations and the order of points allows us to approximate the spatial evolutionary dynamics of the process. This feature shall be useful to interpret the long-term dependence and the memory formed by the spatial history of the process. As an illustration, the sequence can represent the tree locations ordered with respect to time, or to some given quantitative marks such as tree diameters. We derive a parametric sequential spatial point process model that is expressed in terms of self-interaction of the spatial points, and then the maximum-likelihood-based inference is tractable. As an application, we apply the model obtained to forest dataset collected from the Kiihtelysvaara site in Eastern Finland. Potential applications in remote sensing of forests are discussed.