Bayesian joint inference for multiple directed acyclic graphs

Abstract

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 with a known parent ordering 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 joint selection consistency and posterior convergence rates of the fractional posterior in high dimensions. This is the first theoretically supported 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.