Prior and posterior checking of implicit causal assumptions

Causal inference practitioners have increasingly adopted machine learning techniques with the aim of producing principled uncertainty quantification for causal effects while minimizing the risk of model misspecification. Bayesian nonparametric approaches have attracted attention as well, both for their flexibility and their promise of providing natural uncertainty quantification. Priors on high-dimensional or nonparametric spaces, however, can often unintentionally encode prior information that is at odds with substantive knowledge in causal inference-specifically, the regularization required for high-dimensional Bayesian models to work can indirectly imply that the magnitude of the confounding is negligible. In this paper, we explain this problem and provide tools for (i) verifying that the prior distribution does not encode an inductive bias away from confounded models and (ii) verifying that the posterior distribution contains sufficient information to overcome this issue if it exists. We provide a proof-of-concept on simulated data from a high-dimensional probit-ridge regression model, and illustrate on a Bayesian nonparametric decision tree ensemble applied to a large medical expenditure survey.