Bayesian Inference when Parameter Identification is Lacking: A Narrative Arc across Applications, Methods, and Theory

Partially identified models generally yield “in between” statistical behavior. As the sample size goes to infinity, the posterior distribution on the target parameter heads to a distribution narrower than the prior distribution but wider than a single point. Such models arise naturally in many areas, including the health sciences.  They arise particularly  when we own up to limitations in how data are acquired.   I aim to highlight the narrative arc associated with partial identification.   This runs from the applied (e.g., broaching the topic with subject-area scientists), to the methodological (e.g., implementing a Bayesian analysis without full identification), to the theoretical (e.g., characterizing what is going on as generally as possible).  As per many areas of statistics, there is good scope to get involved across the whole arc, rather than just at one end or other.