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 100AGeV+100AGeV Au+Au collisions at the Relativistic Heavy Ion Collider. By simultaneously varying six parameters and by evaluating several classes of observables, we are able to explore the complex intertwined dependencies of observables on model parameters. The methods provide a full multidimensional posterior distribution for the model output, including 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 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. © 2014 American Physical Society.