Bayesian Inference for Partially Identified Models

Identification can be a major issue in causal modeling contexts, and in contexts where observational studies have various limitations. Partially identified models can arise, whereby the identification region for a target parameter -- the set of values consistent with the law of the observable data -- is strictly contained in the set of a priori plausible values, but strictly contains the single true value. The first part of this paper reviews the use of Bayesian inference in partially identified models, and describes the large-sample limit of the posterior distribution over the target parameter. This limiting distribution will have the identification region as its support. The second part of the paper focuses on the informativeness of the shape of the limiting distribution. This provides a point of departure with non-Bayesian approaches, since they focus on inferring the identification region without attempting to speak to relative plausibilities of values inside the identification region. The utility of the shape is investigated in several partially identified models.