  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.
