  Posterior distributions for physical parameters describing relativistic
heavy-ion collisions, such as the viscosity of the quark-gluon plasma, are
extracted through a comparison of hydrodynamic-based transport models to
experimental results from 100$A$ GeV + 100$A$ GeV Au+Au collisions at the
Relativistic Heavy Ion Collider (RHIC). By simultaneously varying six
parameters and by evaluating several classes of observables, we are able to
explore the complex intertwined dependencies of observables to model
parameters. We obtain a full multi-dimensional posterior distribution for the
model output given a large set of experimental observations, the methods
developed here provide a range of acceptable values for each parameter, and
reveal correlations between them. The breadth of observables and the number of
parameters considered here go far beyond previous studies in this field. The
statistical tools, which are based upon Gaussian Process emulators, are tested
in detail and should be extendable to larger data sets and a higher number of
parameters.
