We study the properties of the strongly-coupled quark-gluon plasma with a multistage model of heavy ion collisions that combines the TRENTo initial condition ansatz, free-streaming, viscous relativistic hydrodynamics, and a relativistic hadronic transport. A model-to-data comparison with Bayesian inference is performed, revisiting assumptions made in previous studies. The role of parameter priors is studied in light of their importance towards the interpretation of results. We emphasize the use of closure tests to perform extensive validation of the analysis workflow before comparison with observations. Our study combines measurements from the Large Hadron Collider and the Relativistic Heavy Ion Collider, achieving a good simultaneous description of a wide range of hadronic observables from both colliders. The selected experimental data provide reasonable constraints on the shear and the bulk viscosities of the quark-gluon plasma at T ∼ 150-250 MeV, but their constraining power degrades at higher temperatures T 250 MeV. Furthermore, these viscosity constraints are found to depend significantly on how viscous corrections are handled in the transition from hydrodynamics to the hadronic transport. Several other model parameters, including the free-streaming time, show similar model sensitivity, while the initial condition parameters associated with the TRENTo ansatz are quite robust against variations of the particlization prescription. We also report on the sensitivity of individual observables to the various model parameters. Finally, Bayesian model selection is used to quantitatively compare the agreement with measurements for different sets of model assumptions, including different particlization models and different choices for which parameters are allowed to vary between RHIC and LHC energies. CONTENTS Pratt-Torrieri-Bernhard 10 D. Hadronic transport 11 IV. Specifying prior knowledge 11 V. Bayesian Parameter Estimation with a Statistical Emulator 13 A. Overview of Bayesian Parameter Estimation 13 B. Physical model emulator 14 C. Treatment of uncertainties 16 D. Sampling of the posterior 17 E. Maximizing the posterior 17 VI. Closure Tests 17 A. Validating Bayesian inference with closure tests 18 B. Guiding analyses with closure tests 18 37 A. Full posterior of model parameters 37 B. Posterior for LHC and RHIC independently 37 C. Validation of principal component analysis 37 D. Experimental covariance matrix 38 E. Reducing experimental uncertainty 39 F. Bulk relaxation time 39 G. Comparison to previous studies 40 1. Physics models 41 2. Prior distributions 42 3. Experimental data 42 H. Multistage model validation 42 1. Validation of second-order viscous hydrodynamics implementation 42 a. Validation against cylindrically symmetric external solution 43 2. SMASH 43 3. Comparison of JETSCAPE with hic-eventgen 45 4. The σ meson 46 5. Sampling particles on mass-shell 47 6. QCD equations of state with different hadron resonance gases 47 References 48