  When faced with the task of constraining a galaxy's potential given limited
stellar kinematical information, what is the best way of treating the galaxy's
unknown distribution function (DF)? Using the example of estimating black hole
(BH) masses, I argue that the correct approach is to consider all possible DFs
for each trial potential, marginalizing the DF using an infinitely divisible
prior. Alternative approaches, such as the widely used maximum penalized
likelihood method, neglect the huge degeneracies inherent in the problem and
simply identify a single, special DF for each trial potential.
  Using simulated observations of toy galaxies with realistic amounts of noise,
I find that this marginalization procedure yields significantly tighter
constraints on BH masses than the conventional maximum-likelihood method,
although it does pose a computational challenge which might be solved with the
development of a suitable algorithm for massively parallel machines. I show
that in practice the conventional maximum-likelihood method yields reliable BH
masses with well-defined minima in their chi^2 distributions, contrary to
claims made by Valluri, Merritt & Emsellem.
