Robust Bayesian Inference of Causal Effects via Randomization Distributions

2025-11-01

AI Summary

This paper addresses the limitations of strong modeling assumptions and insufficient robustness in Bayesian causal inference. We propose a general framework grounded in treatment randomization design, which bypasses explicit modeling of the marginal distribution of potential outcomes. Instead, it fixes the observed data and constructs the likelihood directly from the randomization distribution, enabling model-agnostic robust inference. Theoretical contributions include: (i) establishing an intrinsic connection between the posterior mean and classical estimators such as the Hodges–Lehmann estimator; (ii) proving a Bernstein–von Mises theorem and asymptotic consistency; and (iii) supporting posterior model checking as well as flexible extensions—including inverse probability weighting and Hájek estimation. Simulation studies and a nutritional experiment demonstrate that our method effectively uncovers causal heterogeneity undetected by conventional approaches, balancing theoretical rigor with practical interpretability.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We present a general framework for Bayesian inference of causal effects that delivers provably robust inferences founded on design-based randomization of treatments. The framework involves fixing the observed potential outcomes and forming a likelihood based on the randomization distribution of a statistic. The method requires specification of a treatment effect model; in many cases, however, it does not require specification of marginal outcome distributions, resulting in weaker assumptions compared to Bayesian superpopulation-based methods. We show that the framework is compatible with posterior model checking in the form of posterior-averaged randomization tests. We prove several theoretical properties for the method, including a Bernstein-von Mises theorem and large-sample properties of posterior expectations. In particular, we show that the posterior mean is asymptotically equivalent to Hodges-Lehmann estimators, which provides a bridge to many classical estimators in causal inference, including inverse-probability-weighted estimators and Hájek estimators. We evaluate the theory and utility of the framework in simulation and a case study involving a nutrition experiment. In the latter, our framework uncovers strong evidence of effect heterogeneity despite a lack of evidence for moderation effects. The basic framework allows numerous extensions, including the use of covariates, sensitivity analysis, estimation of assignment mechanisms, and generalization to nonbinary treatments.

Problem

• Develops robust Bayesian causal inference via randomization distributions
• Relaxes assumptions compared to superpopulation-based Bayesian methods
• Enables estimation of heterogeneous treatment effects without moderation evidence

Innovation

• Bayesian causal inference via randomization distributions
• Fixes potential outcomes for robust likelihood
• Links posterior mean to Hodges-Lehmann estimators