Bayesian inference of multiple gaussian graphical models

In this paper, we propose a Bayesian approach to inference on multiple Gaussian graphical models. Specifically, we address the problem of inferring multiple undirected networks in situations where some of the networks may be unrelated, while others share common features. We link the estimation of the graph structures via a Markov random field (MRF) prior which encourages common edges. We learn which sample groups have a shared graph structure by placing a spike-and-slab prior on the param-eters that measure network relatedness. This approach allows us to share information between sample groups, when appropriate, as well as to obtain a measure of rela-tive network similarity across groups. Our modeling framework incorporates relevant prior knowledge through an edge-specific informative prior and can encourage simi-larity to an established network. Through simulations, we demonstrate the utility of our method in summarizing relative network similarity and compare its performance against related methods. We find improved accuracy of network estimation, partic-ularly when the sample sizes within each subgroup are moderate. We also illustrate the application of our model to infer protein networks for various cancer subtypes and under different experimental conditions