  In many applications, data often arise from multiple groups that may share
similar characteristics. A joint estimation method that models several groups
simultaneously can be more efficient than estimating parameters in each group
separately. We focus on unraveling the dependence structures of data based on
directed acyclic graphs and propose a Bayesian joint inference method for
multiple graphs. To encourage similar dependence structures across all groups,
a Markov random field prior is adopted. We establish the joint selection
consistency of the fractional posterior in high dimensions, and benefits of the
joint inference are shown under the common support assumption. This is the
first Bayesian method for joint estimation of multiple directed acyclic graphs.
The performance of the proposed method is demonstrated using simulation
studies, and it is shown that our joint inference outperforms other
competitors. We apply our method to an fMRI data for simultaneously inferring
multiple brain functional networks.
