  We apply Markov Chain Monte Carlo to predict the masses required to form the
observed solar $r$-process rare-earth abundance peak. Given highly distinct
astrophysical outflows and nuclear inputs, we find that results are most
sensitive to the $r$-process dynamics (i.e. overall competition between
reactions and decays), with similar mass trends predicted given similar
dynamics. We show that regardless of whether fission deposits into the
rare-earths or not, our algorithm consistently predicts the need for a local
nuclear physics feature of enhanced stability in the neutron-rich lanthanides.
