Sure, with a large data set the problem disappears. I was just wondering how bad my results will be, if I apply a badly chosen prior to a relatively small data set. I realize, of course, that there is no general answer to this question, as it depends on the particular situation. But if you have some useful experience to share, I'm certainly grateful.
Anyway, I will just play around with pyMC3 to get a feel for it. Thanks, and merry Christmas to you, too!