Debiased Bayesian inference for average treatment effects

TL;DR

This paper introduces a data-driven modification to Bayesian methods for estimating average treatment effects, reducing bias and improving accuracy and uncertainty quantification in observational studies.

Contribution

It proposes a novel correction to Bayesian priors based on propensity scores, enhancing causal inference performance in a nonparametric Bayesian framework.

Findings

Significant reduction in bias and improved estimation accuracy.

Enhanced uncertainty quantification compared to unmodified Bayesian methods.

Competitive performance with state-of-the-art causal inference techniques.

Abstract

Bayesian approaches have become increasingly popular in causal inference problems due to their conceptual simplicity, excellent performance and in-built uncertainty quantification ('posterior credible sets'). We investigate Bayesian inference for average treatment effects from observational data, which is a challenging problem due to the missing counterfactuals and selection bias. Working in the standard potential outcomes framework, we propose a data-driven modification to an arbitrary (nonparametric) prior based on the propensity score that corrects for the first-order posterior bias, thereby improving performance. We illustrate our method for Gaussian process (GP) priors using (semi-)synthetic data. Our experiments demonstrate significant improvement in both estimation accuracy and uncertainty quantification compared to the unmodified GP, rendering our approach highly competitive with the state-of-the-art.