Ryan Giordano, Tamara Broderick, and Michael Jordan write:
In Bayesian analysis, the posterior follows from the data and a choice of a prior and a likelihood. One hopes that the posterior is robust to reasonable variation in the choice of prior, since this choice is made by the modeler and is often somewhat subjective. A different, equally subjectively plausible choice of prior may result in a substantially different posterior, and so different conclusions drawn from the data. . . .
To which I say:
,s/choice of prior/choice of prior and data model/g
Yes, the choice of data model (from which comes the likelihood) is made by the modeler and is often somewhat subjective. In those cases where the data model is not chosen subjectively by the modeler, it is typically chosen implicitly by convention, and there is even more reason to be concern about robustness.