Primary Submission Category: Bayesian Causal Inference
Density Regression Bayesian Causal Forests
Authors: Anna Morgan, Jared Murray,
Presenting Author: Anna Morgan*
We introduce a nonparametric Bayesian approach for estimating heterogeneous effects with density regression, building upon Bayesian Causal Forests (BCF) and prior Bayesian Additive Regression Trees (BART) density regression methods. We incorporate a targeted smoothing prior on terminal tree nodes to ensure smoothness and a reduced-rank kernel approximation to make (approximate) Gaussian process regression computationally feasible. Allowing distributional features of the response density to vary with covariates relaxes strong assumptions about the treatment effect mechanism and allows for richer insights about treatment effect heterogeneity. We illustrate our model by applying it to data from a recent high-profile mindset intervention experiment, allowing new exploration of differential treatment effect patterns and subgroups of interest. Finally, we carefully consider prior specification and the implied regularization on treatment effects of interest to tune our model for causal inference in a realistic setting. We propose reasonable default priors for parameters of the treatment effect function and discuss how these priors may be informed by beliefs about the potential scale of treatment effects, illustrated by simulation studies.