  In this article, we propose a new class of priors for Bayesian inference with
multiple Gaussian graphical models. We introduce fully Bayesian treatments of
two popular procedures, the group graphical lasso and the fused graphical
lasso, and extend them to a continuous spike-and-slab framework to allow
self-adaptive shrinkage and model selection simultaneously. We develop an EM
algorithm that performs fast and dynamic explorations of posterior modes. Our
approach selects sparse models efficiently with substantially smaller bias than
would be induced by alternative regularization procedures. The performance of
the proposed methods are demonstrated through simulation and two real data
examples.
