Bayesian Estimation of Single and Multiple Graphs

In this chapter, we discuss Bayesian approaches for the inference of both single and multiple networks. To begin, we provide an overview of Bayesian graphical modeling approaches to learn directed and undirected networks, from either Gaussian or non-Gaussian data. We then provide an in-depth description of Bayesian models for the joint estimation of multiple undirected networks, where either the inclusion of edges or the edge values themselves are related across settings. These approaches highlight some of the advantages of taking a Bayesian approach, as hierarchical priors enable sharing of information across groups, automatic learning of parameters, and posterior estimates of uncertainty regarding individual networks and their similarity. We include simulation studies comparing the performance of Bayesian and frequentist methods for the inference of multiple networks, as well as a case study on brain structural connectivity networks during the progression of Alzheimer's disease.