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 article, 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 fixeddimensional 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. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory

Bayesian causal inference: a critical review

“…Research on Bayesian analysis of these topics has been rapidly increasing [10,[112][113][114][115] and is expected to continue to grow.…”

“…Other Bayesian non-parametric models, such as Gaussian process [47], Dirichlet process [48][49][50][51], have also been considered for causal inference. We refer interested readers to [10] for a more detailed review of these methods.…”

“…When there are a large number of covariates, the Bayesian paradigm usually achieves regularization through sparsity-inducing priors for the outcome model, such as the spike-andslab prior [55], the Bayesian LASSO [56], as well as the model averaging techniques [57][58][59]. The use of these methods in causal inference is surveyed in [10,50]. High-dimensional covariates pose additional complications to Bayesian causal inference.…”

“…The Bayesian approach has several established advantages for general statistical analysis, including automatic uncertainty quantification, coherently incorporating prior knowledge, and offering a rich collection of advanced models for complex data. As causal studies increasingly involve real-world big data, there has been a recent surge of research in Bayesian inference of causal effects [7][8][9][10][11], but there is no comprehensive appraisal of the current state of the research. This paper aims to fill this gap.…”

A reference-free R-learner for treatment recommendation

“…30 Recently, there is a growing interest in estimating the response surfaces through the Bayesian framework due to its competitive performance. [31][32][33][34][35] While intuitive in concept, these learners provide no performance guarantee in the presence of strong group size variation, especially when the response surfaces are trained separately. 28,36 One could directly target the contrast of treatment effects and use the combined sample to alleviate the estimation bias.…”