  This work presents a Bayesian inference study for relativistic heavy-ion
collisions in the Beam Energy Scan program at the Relativistic Heavy-Ion
Collider. The theoretical model simulates event-by-event (3+1)D collision
dynamics using hydrodynamics and hadronic transport theory. We analyze the
model's 20-dimensional posterior distributions obtained using three model
emulators with different accuracy and demonstrate the essential role of
training an accurate model emulator in the Bayesian analysis. Our analysis
provides robust constraints on the Quark-Gluon Plasma's transport properties
and various aspects of (3+1)D relativistic nuclear dynamics. By running full
model simulations with 100 parameter sets sampled from the posterior
distribution, we make predictions for $p_{\rm T}$-differential observables and
estimate their systematic theory uncertainty. A sensitivity analysis is
performed to elucidate how individual experimental observables respond to
different model parameters, providing useful physics insights into the
phenomenological model for heavy-ion collisions.
