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

Methodology