Discussion of ‘Modern Statistics for Spatial Point Processes’

Abstract

Abstract. The paper ‘Modern statistics for spatial point processes’ by Jesper Møller and Rasmus P. Waagepetersen is based on a special invited lecture given by the authors at the 21st Nordic Conference on Mathematical Statistics, held at Rebild, Denmark, in June 2006. At the conference, Antti Penttinen and Eva B. Vedel Jensen were invited to discuss the paper. We here present the comments from the two invited discussants and from a number of other scholars, as well as the authors’ responses to these comments. Below Figure 1, Figure 2, etc., refer to figures in the paper under discussion, whileFigure A,Figure B, etc., refer to figures in the current discussion. All numbered sections and formulas refer to the paper. The estimate ofA(k) (solid curve) and pointwise maximum and minimum envelopes (dotted curves) from 99 simulations under independent marking, conditional on the point locations. Zero boundary has been applied.image Examples of realizations of inhomogeneous shot noise Cox processes. The (mean) intensity function is the same in all three examples. To the left, the inhomogeneity is introduced via the location of the mothers in Φ, in the middle the inhomogeneity is obtained by a location dependent thinning of a homogeneous Cox process while to the right the inhomogeneity is obtained by a local scaling mechanism.imageThe Editors