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.

Confounder-Dependent Bayesian Mixture Model: Characterizing Heterogeneity of Causal Effects in Air Pollution Epidemiology

“…Bayesian nonparametric (BNP) approaches are known for their flexibility to adapt to different contexts (Escobar and West, 1995;Green and Richardson, 2001;Hjort et al, 2010). However, despite this flexibility, the literature on BNP methods for causal inference, and particularly for identifying factors that contribute to heterogeneity of causal effects, is relatively recent (Linero and Antonelli, 2021). Researchers in this field have focused on the application or extension of the Bayesian Additive Regression Tree (BART) (Chipman et al, 2010), and dependent Dirichlet Process (DDP) mixture models (MacEachern, 2000;Barrientos et al, 2012;Quintana et al, 2022) to the causal inference framework.…”

“…Notably, the Enriched Dirichlet process mixture model (Wade et al, 2011(Wade et al, , 2014 and its modifications have found extensive and promising causal applications (Roy et al, 2018;Oganisian et al, 2020aOganisian et al, ,b, 2021. For a review of BNP applications in causal inference, we refer to Linero and Antonelli (2021).…”