Bayesian Inverse Probability Weighting

Bayesian Inverse Probability Weighting (Bayesian IPW) extends the classical IPW estimator by placing prior distributions over the propensity-score model parameters and propagating that uncertainty into the causal-effect estimate. The result is a posterior distribution for the average treatment effect that fully accounts for both propensity-score estimation uncertainty and outcome-model uncertainty, enabling credible-interval inference rather than relying on asymptotic approximations.