  We introduce a model for heavy ion collisions named Trajectum, which includes
an expanded initial stage with a variable free streaming velocity $v_{\rm fs}$
and a hydrodynamic stage with three varying second order transport
coefficients. We describe how to obtain a Gaussian Emulator for this
20-parameter model and show results for key observables. This emulator can be
used to obtain Bayesian posterior estimates on the parameters, which we test by
an elaborate closure test as well as a convergence study. Lastly, we employ the
optimal values of the parameters found in [1] to perform a detailed comparison
to experimental data from PbPb and $p$Pb collisions. This includes both
observables that have been used to obtain these values as well as wider
transverse momentum ranges and new observables such as correlations of
event-plane angles.
