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In causal estimation problems, the parameter of interest is often onlypartially identified, implying that the parameter cannot be recovered exactly,even with infinite data. Here, we study Bayesian inference for partiallyidentified treatment effects in multi-treatment causal inference problems withunobserved confounding. In principle, inferring the partially identifiedtreatment effects is natural under the Bayesian paradigm, but the results canbe highly sensitive to parameterization and prior specification, often insurprising ways. It is thus essential to understand which aspects of theconclusions about treatment effects are driven entirely by the priorspecification. We use a so-called transparent parameterization to contextualizethe effects of more interpretable scientifically motivated prior specificationson the multiple effects. We demonstrate our analysis in an example quantifyingthe effects of gene expression levels on mouse obesity.

Bayesian Inference and Partial Identification in Multi-Treatment Causal Inference with Unobserved Confounding