thank you very much for your answers @ricardoV94 and @jessegrabowski , they make perfectly sense. But I wonder. Having a mode at boundary (zero in this case) for a prior/posterior distribution should be a pretty common case. Take for example the non-centered 8-school problem formulation. \tau is sampled according to a halfCauchy distribution here:
and these are the posteriors of the parameters (I guess you can ignore variables other than tau in the picture)
Shouldn’t I end up with divergences then in this case (and all other similar cases)?