  In this paper we propose a class of prior distributions on decomposable
graphs, allowing for improved modeling flexibility. While existing methods
solely penalize the number of edges, the proposed work empowers practitioners
to control clustering, level of separation, and other features of the graph.
Emphasis is placed on a particular prior distribution which derives its
motivation from the class of product partition models; the properties of this
prior relative to existing priors is examined through theory and simulation. We
then demonstrate the use of graphical models in the field of agriculture,
showing how the proposed prior distribution alleviates the inflexibility of
previous approaches in properly modeling the interactions between the yield of
different crop varieties.
