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Abstract:
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In observational studies, there are many ways in which the data we actually have can differ from the data we wish we had. For instance, relevant variables may be poorly measured, or even entirely absent. It may be possible to construct a reasonable model for how the actual data relate to the ideal data, as an adjunct to the model of interest for the ideal data. Often, however, the implied model for the actual data is not identified. We discuss the mechanics of Bayesian inference when the model is nonidentified, and the added value of a Bayesian analysis relative to a sensitivity analysis in this context. Also, in the specific case of unobserved confounding, we consider the impact of an a priori judgment that observed and unobserved confounders are exchangeable.
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