The How and Why of Bayesian Nonparametric Causal Inference

Abstract: Spurred on by recent successes in causal inference competitions, Bayesian nonparametric (and high-dimensional) methods have recently seen increased attention in the causal inference literature. In this paper, we present a comprehensive overview of Bayesian nonparametric applications to causal inference. Our aims are to (i) introduce the fundamental Bayesian nonparametric toolkit; (ii) discuss how to determine which tool is most appropriate for a given problem; and (iii) show how to avoid common pitfalls in applying Bayesian nonparametric methods in high-dimensional settings. Unlike standard fixed-dimensional parametric problems, where outcome modeling alone can sometimes be effective, we argue that most of the time it is necessary to model both the selection and outcome processes.