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

TL;DR

This paper introduces a flexible Bayesian nonparametric method for estimating population and conditional causal effects from observational data, effectively adjusting for confounders and capturing treatment heterogeneity.

Contribution

It develops a dependent nonparametric mixture model that models the outcome distribution conditioned on confounders without parametric assumptions, improving causal effect estimation.

Findings

Outperforms existing methods like BART in simulations.

Provides fully probabilistic inference for causal effects.

Efficient posterior computation with data augmentation.

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.