Bridging the design and modeling of causal inference: A Bayesian nonparametric perspective

In their seminal paper first published 40 years ago, Rosenbaum and Rubin crafted the concept of the propensity score to tackle the challenging problem of causal inference in observational studies. The propensity score is set up mostly as a design tool to recreate a randomization like scenario, through matching or subclassification. Bayesian development over the past two decades has adopted a modeling framework to infer the causal effect. In this commentary, we highlight the connection between the design-and model-based perspectives to analysis. We briefly review a Bayesian nonparametric framework that utilizes Gaussian Process models on propensity scores to mimic matched designs. We also discuss the role of variation as well as bias in estimators arising from observational data.