  Motivated by the need to study the molecular mechanism underlying Type 1
Diabetes (T1D) with the gene expression data collected from both the patients
and healthy controls at multiple time points, we propose an innovative method
for jointly estimating multiple dependent Gaussian graphical models. Compared
to the existing methods, the proposed method has a few significant advantages.
First, it includes a meta-analysis procedure to explicitly integrate
information across distinct conditions. In contrast, the existing methods often
integrate information through prior distributions or penalty function, which is
usually less efficient. Second, instead of working on original data, the
Bayesian step of the proposed method works on edge-wise scores, through which
the proposed method avoids to invert high-dimensional covariance matrices and
thus can perform very fast. The edge-wise score forms an equivalent measure of
the partial correlation coefficient and thus provides a good summary for the
graph structure information contained in the data under each condition. Third,
the proposed method can provide an overall uncertainty measure for the edges
detected in multiple graphical models, while the existing methods only produce
a point estimate or are feasible for very small size problems. We prove
consistency of the proposed method under mild conditions and illustrate its
performance using simulated and real data examples. The numerical results
indicate the superiority of the proposed method over the existing ones in both
estimation accuracy and computational efficiency. Extension of the proposed
method to joint estimation of multiple mixed graphical models is
straightforward.
