Objective methods for graphical structural learning

Graphical models are used for expressing conditional independence relationships among variables by the means of graphs, whose structure is typically unknown and must be inferred by the data at hand. We propose a theoretically sound Objective Bayes procedure for graphical model selection. Our method is based on the Expected-Posterior Prior and on the Power-Expected-Posterior Prior. We use as input of the proposed methodology a default improper prior and suggest computationally efficient approximations of Bayes factors and posterior odds. In a variety of simulated scenarios with varying number of nodes and sample sizes, we show that our method is highly competitive with, or better than, current benchmarks. We also discuss an application to protein-signaling data, which wieldy confirms existing results in the scientific literature.