Bayesian multiple Gaussian graphical models for multilevel variables from unknown classes

Gaussian graphical models are a powerful tool for investigating the conditional dependency structure between random variables by estimating sparse precision matrices and can infer networks among variables from multiple classes. Many studies assume that classes of observations are given and use methods to learn the network structures within one level (e.g. pathways or genes). In most cases, however, heterogeneous data may be obtained at different levels. Therefore, in this paper, we consider the learning of multiple connected graphs with multilevel variables from unknown classes. We estimate the classes of the observations from the mixture distributions by evaluating the Bayes factor and learn about the network structures by fitting a neighborhood-selection algorithm. This approach can be used to identify the class memberships and reveal the network structures for lower level and higher level variables simultaneously. Unlike most existing methods, which solve this problem using frequentest approaches, we assess an alternative and novel hierarchical Bayesian approach for incorporating prior knowledge. We demonstrate the unique advantages of our methods through several simulations. A breast cancer application shows that our model's results can provide insight into biological studies.