Bayesian Methods for Causal Inference

Specialeforsvar: Clara Rosengaard Groth

Titel: Bayesian Methods for Causal Inference

Abstract: This thesis investigates Bayesian methods for causal inference based on the potential outcomes framework. Historically, frequentist methods have dominated, so we first introduce the frequentist framework focusing on double robust estimation in semi-and nonparametric regression settings. We then provide a fully Bayesian probabilistic formulation of potential outcome models, explicitly define the assumptions needed for causal identification, and highlight the unique philosophical and practical challenges in the Bayesian framework. Special attention is given to (i) the use of propensity scores and (ii) the limitations of a "dogmatic" Bayesian approach that estimates treatment and outcome models simultaneously, which induces feedback. This phenomenon is demonstrated through a simple linear regression simulation. We review recent work extending the double robust estimation framework to a Bayesian setup using Gaussian process regression, which preserves posterior uncertainty quantification. This approach is examined both theoretically, by reproducing the proof of double robustness, and empirically, through a simulation study comparing frequentist AIPW-DML estimators, the Bayesian double robust (BDR) estimator, and an estimator using Bayesian additive regression trees (BART). Our findings suggest, that while Bayesian methodologies are powerful, they do not consistently outperform frequentist methods in practice.

Vejleder: Anton Rask Lundborg

Censor: Søren Wengel Mogensen