Bayesian clustering in decomposable graphs

TL;DR

This paper introduces a new class of prior distributions for decomposable graphs that enhances modeling flexibility by allowing control over clustering and separation, with applications demonstrated in agricultural crop yield interactions.

Contribution

It proposes a novel prior based on product partition models, improving upon existing edge-penalizing methods for decomposable graphs.

Findings

The new prior offers greater flexibility in graph modeling.

Theoretical and simulation analysis compare properties with existing priors.

Application to agriculture shows improved modeling of crop yield interactions.

Abstract

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.