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The advent of multiple successfully calibrated models for relativistic heavy-ion collisions demands a clear strategy based on rigorous statistical principles to utilize them all in understanding the nature of the quark-gluon plasma. The successful calibration of the viscous anisotropic hydrodynamic model in this thesis adds another serious competitor to the arena and emphasizes, even more, the importance of such a unifying strategy. In our work, we have identifed the need for massive computational resources as one of the main challenges to studying relativistic heavy-ion collisions using multiple simulation models. We introduce multiple novel computational tools that can be used in our feld of study to ease this computational burden. Lastly, we discuss a novel Bayesian model mixing tool developed by us, Taweret, which can combine multiple diferent simulations to obtain more accurate predictions. For the frst time, we apply these model mixing techniques to locally mix two models from relativistic heavy-ion collisions with mixing weights that vary with collision centrality. Furthermore, we perform a Bayesian parameter estimation with the mixed model to infer the properties of the quark-gluon plasma considering both the experimental and modeling uncertainties. It is our hope that this work provides clear directions for future studies of the quark-gluon plasma fluid created in laboratory experiments, making use of multiple models and the full set of experimental data.