Credible Bounds for Causal Quantities with Continuous Outcomes

The problem of partial identification concerns bounding causal quantities that remain unidentifiable given the observed distribution and the causal diagram of the underlying structural causal model (SCM). While bounds have been developed for certain causal quantities with continuous outcomes, they are necessarily univariate and are unable to reflect differing levels of confidence. Building on previous work in partial identification, we propose a simple Bayesian method for deriving probabilistic bounds on a large class of causal quantities with potentially multivariate and/or continuous outcome variables.