Title: A Bayesian Approach for Estimating Causal Effects from Observational Data
Abstract: We present a Bayesian method for the challenging task of estimating causal effects from passively observed data when the underlying causal DAG structure is unknown. To capture the inherent uncertainty associated with the estimate, our method builds a Bayesian posterior distribution of the linear causal effect, by integrating Bayesian linear regression and averaging over DAGs. For computing the exact posterior for all cause-effect variable pairs, we give an algorithm that runs in time $O(3^d d)$ for $d$ variables, being feasible up to 20 variables. We also give a variant that computes the posterior probabilities of all pairwise ancestor relations within the same time complexity, significantly improving the fastest previous algorithm. In simulations, our method performs favorably against previous methods in estimation accuracy, especially for small sample sizes.
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