Limiting Stochastic Processes for Spatial Structure Detection

Abstract: Data showing spatial structure often arise in many applied scientific fields in form of points spatially distributed within a planar region. The basic methodology for analyzing spatial point pattern data is well established though most of the literature does not deal with point processes coming from the limit of lattice processes. However, spatial point processes that can be obtained from the limit of a suitable sequence of auto-Poisson stochastic lattice processes can be regarded as a useful tool to analyze spatial patterns exhibiting random and ordered structures. In this paper, we present a theoretical and computational framework and develop some practical issues in terms of a simulation study and real-data analysis.