title: Mechanistic spatio-temporal point process models for marked point processes, with a view to forest stand data.
abstract: We show how a spatial point process, where to each point there is associated a random quantitative mark, can be identified with a spatio-temporal point process specified by a conditional intensity function. For instance, the points can be tree locations, the marks can express the size of trees, and the conditional intensity function can describe the distribution of a tree (i.e., its location and size) conditionally on the larger trees. This enable us to construct parametric statistical models which are easily interpretable and where maximum-likelihood-based inference is tractable.
authors.affiliation: Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark. jm@math.aau.dk.
authors.forename: Jesper
authors.initials: J
authors.lastname: Møller
authors.affiliation: Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark.
authors.forename: Mohammad
authors.initials: M
authors.lastname: Ghorbani
authors.affiliation: Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark.
authors.forename: Ege
authors.initials: E
authors.lastname: Rubak
mesh_terms: D003198:Computer Simulation; D065928:Forests; D016013:Likelihood Functions; D008954:Models, Biological; D015233:Models, Statistical; D028223:Pinus / Q000254:growth & development; D062211:Spatio-Temporal Analysis
keywords: Conditional intensity; Independence between points and marks; Likelihood ratio statistic; Maximum likelihood; Model checking; Quantitative marks