A0947
Title: Double robust Bayesian inference on average treatment effects
Authors: Ruixuan Liu - Chinese University of Hong Kong (Hong Kong) [presenting]
Abstract: A double robust Bayesian inference procedure is proposed on the average treatment effect under unconfoundedness. The robust Bayesian approach involves two important modifications: first, the prior distributions of the conditional mean function are adjusted; second, the posterior distribution of the resulting ATE is corrected. Both adjustments make use of pilot estimators motivated by the semiparametric influence function for ATE estimation. Asymptotic equivalence of the Bayesian procedure and efficient frequentist ATE estimators are proven by establishing a new semiparametric Bernstein-von Mises theorem under double robustness, i.e., the lack of smoothness of conditional mean functions can be compensated by high regularity of the propensity score and vice versa. Consequently, the resulting Bayesian credible sets form confidence intervals with asymptotically exact coverage probability. In simulations, our double robust Bayesian procedure leads to significant bias reduction of point estimation over conventional Bayesian methods and more accurate coverage of confidence intervals compared to existing frequentist methods. The method is illustrated in an application to the national supported work demonstration.
