Bayesian Nonparametrics, Informative Priors, and Causal Inference
*Michael J Daniels, University of Texas at Austin
Keywords: Bayesian inference, mediation
Except in very simple situations, untestable (from the observed data) assumptions need to be made for drawing causal inferences. Similar to missing data problems, the problem can be partitioned into two components: 1) a model for the observed data and 2) a set of (reasonable) assumptions that allow identification and estimation of causal estimands given the observed data. Given that the second component is not checkable from the observed data, uncertainty about these assumptions are essential for a fair characterization of the uncertainty. We contend that these two components can be handled most naturally in the Bayesian paradigm using flexible Bayesian nonparametric (BNP) models for the observed data and assumptions with sensitivity parameters that can be specified with informative priors. BNP models will provide similar robustness to semiparametric approaches. We provide an illustration of this approach in the setting of the causal effect of mediation.