A General Bayesian Nonparametric Approach for Estimating Population-Level and Conditional Causal Effects

Abstract

We propose a Bayesian nonparametric (BNP) approach to causal inference using observational data consisting of outcome, treatment, and a set of confounders. The conditional distribution of the outcome given treatment and confounders is modeled flexibly using a dependent nonparametric mixture model, in which both the atoms and the weights vary with the confounders. The proposed BNP model is well suited for causal inference problems, as it does not rely on parametric assumptions about how the conditional distribution depends on the confounders. In particular, the model effectively adjusts for confounding and improves the modeling of treatment effect heterogeneity, leading to more accurate estimation of both the average treatment effect (ATE) and heterogeneous treatment effects (HTE). Posterior inference under the proposed model is computationally efficient due to the use of data augmentation. Extensive evaluations demonstrate that the proposed model offers competitive or superior performance compared to a wide range of recent methods spanning various statistical approaches, including Bayesian additive regression tree (BART) models, which are well known for their strong empirical performance. More importantly, the model provides fully probabilistic inference on quantities of interest that other methods cannot easily provide, using their posterior distributions.