Bayesian Models and Methods for Counterfactual Prediction and Causal Inference

Simultaneous graphical dynamic linear models (SGDLMs) provide advances in flexibility, parsimony and scalability of multivariate time series analysis, with proven utility in forecasting. Core theoretical aspects of such models are developed, including new results linking dynamic graphical and latent factor models. Methodological developments extend existing Bayesian sequential analyses for model marginal likelihood evaluation and counterfactual forecasting. The latter, involving new Bayesian computational developments for missing data in SGDLMs, is motivated by causal applications. A detailed example concerns the effect of the Affordable Care Act's Medicaid expansion on employment, with advances in model uncertainty and staggered adoptions.

This is joint work with Mike West.
 

I will discuss various topics at the intersection of machine learning, Bayesian methods, and the estimation of causal effects, focusing on the estimation of conditional average treatment effects (CATEs). I make the following claims:

1. Judicious, direct, regularization of the treatment effect heterogeneity is essential to get low-RMSE estimates of the CATE, and in high-noise settings this can be more important than specifying the functional form of the model correctly.

2. Bayesian decision tree ensembles with causally-informed priors, that both shrink towards homogeneous treatment effects and incorporate the propensity score, typically perform very well in this context relative to meta-learning approaches; in particular, estimation accuracy for CATEs is high and uncertainty quantification is conservative in the sense of being biased against finding non-existent heterogeneity.

3. Naive applications of Bayesian machine learning approaches typically lead to poor frequentist performance. We observe that naive approaches tend to also be deficient from a subjective Bayesian perspective, in that they imply tightly-concentrated prior distributions on certain selection bias parameters that we actually wish to express ignorance about.

Our points are illustrated through analysis of both data-informed simulations and analysis of medical expenditure data.
 

Principal stratification provides a causal inference framework that allows adjustment for confounded post-treatment variables when comparing treatments. Although the literature has focused mainly on binary post-treatment variables, there is a growing interest in principal stratification involving continuous post-treatment variables. However, characterizing the latent principal strata with a continuous post-treatment presents a significant challenge, which is further complicated in observational studies where the treatment is not randomized. In this paper, we introduce the Confounders-Aware SHared atoms BAyesian mixture (CASBAH), a novel approach for principal stratification with continuous post-treatment variables that can be directly applied to observational studies. CASBAH leverages a dependent Dirichlet process—utilizing shared atoms across treatment levels—to effectively control for measured confounders and facilitate information sharing between treatment groups in the identification of principal strata membership. CASBAH also offers a comprehensive quantification of uncertainty surrounding the membership of the principal strata. Through Monte Carlo simulations, we show that the proposed methodology has excellent performance in characterizing the latent principal strata and estimating the effects of treatment on post-treatment variables and outcomes. Finally, CASBAH is applied to a case study in which we estimate the causal effects of US national air quality regulations on pollution levels and health outcomes.

This is joint work with Antonio Canale, Fabrizia Mealli and Francesca Dominici.