Comment on article by Scutari

We congratulate the author for a well-written article on a problem of clear and increasing scientific relevance. The approach taken here is not only relevant for prior specification and analysis of posterior distributions in graphical models, but has a much wider breadth as explained below. In his work on Bayesian inference of graphical models, the author adopts a novel focus on prior formulations over binary or trinary indicators of edge inclusion in undirected or directed graphs, and examines relevant properties of these distributions including entropy and variability. The insights of this paper provide a valuable starting point for further exploration of the proposed priors both in terms of theoretical properties and practical application to real or simulated data. Although we do not see how the proposed parametrization reduces the dimension of the parameter space, we consider the approach taken in this work a novel point of view both in terms of defining prior distributions over a set of dependent binary and trinary random variables and in terms of analyzing the posterior distributions of those variables.