Toward a deeper understanding of how experiments constrain the underlying physics of heavy-ion collisions

Recent work has provided the means to rigorously determine properties of superhadronic matter from experimental data through the application of broad scale modeling of high-energy nuclear collisions within a Bayesian framework. These studies have provided unprecedented statistical inferences about the physics underlying nuclear collisions by virtue of simultaneously considering a wide range of model parameters and experimental observables. Notably, this approach has been used to constrain both the QCD equation of state and the shear viscosity above the quark-hadron transition. Although the inferences themselves have a clear meaning, the complex nature of the relationships between model parameters and observables has remained relatively obscure. We present here a novel extension of the standard Bayesian Markov-chain Monte Carlo approach that allows for the quantitative determination of how inferences of model parameters are driven by experimental measurements and their uncertainties. This technique is then applied in the context of heavy-ion collisions in order to explore previous results in greater depth. The resulting relationships are useful for identifying model weaknesses, prioritizing future experimental measurements, and, most importantly, developing an intuition for the roles that different observables play in constraining our understanding of the underlying physics.