We start with a brief review of Bayesian techniques for the analysis of multiple graphical models and then move to recent inferential and computational techniques for multiple graphical models, where the sub-group assignment depends on the value of an externally observed covariate. We then introduce Bayesian Gaussian graphical models with covariates (GGMx), a class of multivariate Gaussian distributions with covariate-dependent sparse precision matrix. We propose a general construction of a functional mapping from the covariate space to the cone of sparse positive definite matrices encompassing many existing graphical models for heterogeneous settings. The flexible formulation of GGMx allows both the strength and the sparsity pattern of the precision matrix (hence the graph structure) to change with the covariates. Extensive simulations and a cancer genomics case study demonstrate the proposed models' utility.
