Graphical modelling of multivariate spatial point processes

TL;DR

This paper introduces a new graphical model for analyzing the complex dependence structure of multivariate spatial point processes, enabling simultaneous analysis of all interrelations in high-dimensional spatial data.

Contribution

It presents the spatial dependence graph model that uses conditional partial spectral coherence to capture global dependence structures, a novel approach in spatial point process analysis.

Findings

Effective analysis of forest stand data

Application to crime data in London

Demonstrates high-dimensional dependence modeling

Abstract

This paper proposes a novel graphical model, termed the spatial dependence graph model, which captures the global dependence structure of different events that occur randomly in space. In the spatial dependence graph model, the edge set is identified by using the conditional partial spectral coherence. Thereby, nodes are related to the components of a multivariate spatial point process and edges express orthogonality relation between the single components. This paper introduces an efficient approach towards pattern analysis of highly structured and high dimensional spatial point processes. Unlike all previous methods, our new model permits the simultaneous analysis of all multivariate conditional interrelations. The potential of our new technique to investigate multivariate structural relations is illustrated using data on forest stands in Lansing Woods as well as monthly data on crimes committed in the City of London.