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In many applications, data often arise from multiple groups that may sharesimilar characteristics. A joint estimation method that models several groupssimultaneously can be more efficient than estimating parameters in each groupseparately. We focus on unraveling the dependence structures of data based ondirected acyclic graphs and propose a Bayesian joint inference method formultiple graphs. To encourage similar dependence structures across all groups,a Markov random field prior is adopted. We establish the joint selectionconsistency of the fractional posterior in high dimensions, and benefits of thejoint inference are shown under the common support assumption. This is thefirst Bayesian method for joint estimation of multiple directed acyclic graphs.The performance of the proposed method is demonstrated using simulationstudies, and it is shown that our joint inference outperforms othercompetitors. We apply our method to an fMRI data for simultaneously inferringmultiple brain functional networks.

Bayesian joint inference for multiple directed acyclic graphs