Tessellated spatial Poisson point process models

Abstract

A novel framework for the local modelling of spatial point processes is proposed by extending segmented regression models to spatial contexts. The approach consists of a two-step procedure: first, a spatial segmentation algorithm identifies a spatial tessellation using geographically weighted regression estimates; then, a log-linear Poisson model is fitted within the identified non-overlapping regions. This methodology can serve for spatial breakpoint detection or as a local spatial modeling tool. The method is illustrated by a case study on seismicity.