  The quality of data taken at RHIC and LHC as well as the success and
sophistication of computational models for the description of
ultra-relativistic heavy-ion collisions have advanced to a level that allows
for the quantitative extraction of the transport properties of the
Quark-Gluon-Plasma. However, the complexity of this task as well as the
computational effort associated with it can only be overcome by developing
novel methodologies: in this paper we outline such an analysis based on
Bayesian Statistics and systematically compare an event-by-event heavy-ion
collision model to data from the Large Hadron Collider. We simultaneously probe
multiple model parameters including fundamental quark-gluon plasma properties
such as the temperature-dependence of the specific shear viscosity $\eta/s$,
calibrate the model to optimally reproduce experimental data, and extract
quantitative constraints for all parameters simultaneously. The method is
universal and easily extensible to other data and collision models.
