Partially identified models generally yield “in between” 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 point-mass. Such models arise naturally in many areas, including public health and epidemiology. As exemplars, we describe two models recently applied to pandemic data. One involves inferring an epidemic curve in light of an imperfect diagnostic test with imperfect knowledge of its imperfections. The other involves meta-analytic inference about infection fatality rates, via a combination of surveillance data and sero-survey data. We use these as examples to comment on general issues with Bayesian inference in partially identified models. We focus on information flow, investigating how much can we realistically expect to learn without the benefit of full identification.