Primary Submission Category: Bayesian Causal Inference
Extending general BART with Pitman-Yor mixtures: novel nonparametric prior to correct for strong unobserved confounding
Authors: Andrej Srakar, Marilena Vecco,
Presenting Author: Andrej Srakar*
Bayesian additive regression trees (BART) perspective has been developed by Chipman et al. (2010) and popularized in its usage in causal inference problems. It commonly uses a specific regularization prior, sometimes combined with Gaussian, Dirichlet, Dirichlet Process Mixture and semiparametric perspectives in a general BART perspective (Tan and Roy, 2019). Despite its success there has been a growing number of papers that point out its limitations. We develop a novel nonparametric regularization prior for BART based on Pitman-Yor Mixture (PYM) partition-based process standard error structure, which has to date to our knowledge rarely been used in causal inference. Our novel perspective is studied for several causal perspectives: regression discontinuity design; causal maximally partially directed acyclic graph; direct causal clause; and causal mediation. Study of asymptotic properties in a Bayesian framework extends recent proposal of Jeong and Rockova (2022) of sparse piecewise heterogeneous anisotropic Hölder functions to account for anisotropic regions in general BART. Results on simulated and real data confirm improved properties compared to earlier BART priors in particular in the presence of strong confounding. We address computational issues by using importance sampling with the integrated nested Laplace approximation (Outzen Berild et al., 2021). We discuss extensions to endogeneity corrections and Single World Intervention Graph perspective.