Bayesian Inference of Multiple Gaussian Graphical Models

• Activity Number: 221
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Christine Peterson*+ and Francesco Stingo and Marina Vannucci
• Companies: Stanford University and MD Anderson Cancer Center and Rice University
• Keywords: Gaussian graphical model ; Markov random field ; network inference ; G-Wishart prior ; multiple networks

Abstract

In this work, we propose a Bayesian approach for inference of 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 prior which encourages common edges. In addition, we learn which sample groups have shared graph structure by placing a spike-and-slab prior on the parameters that measure network relatedness. This approach allows us to share information between sample groups, when appropriate, as well as to obtain a measure of relative network similarity across groups. In simulation studies, we find improved accuracy of network estimation over competing methods, particularly when the sample sizes within each subgroup are moderate. We illustrate our model with an application to inference of protein networks for various subtypes of acute myeloid leukemia.