  The study of heavy-ion collisions presents a challenge to both theoretical
and experimental nuclear physics. Due to the extremely short lifetime and small
size of the collision system, disentangling information provided by
experimental observables and progress in physical insight requires the careful
application of plausible reasoning. I apply a program of statistical
methodologies, primarily Bayesian, to quantify properties of the medium in
specific models, as well as compare and criticize differing models of the
system. Of particular interest are estimations of the specific shear and bulk
viscosities, where we find that information carried by the experimental data is
still limited. In particular we find a large sensitivity to prior assumptions
at high temperatures. Moreover, sensitivities to model assumptions are present
at low temperatures, and this source of model uncertainty is propagated with
model averaging and model mixing.
