  Bayesian parameter estimation provides a systematic approach to compare heavy
ion collision models with measurements, leading to constraints on the
properties of nuclear matter with proper accounting of experimental and
theoretical uncertainties. Aside from statistical and systematic model
uncertainties, interpolation uncertainties can also play a role in Bayesian
inference, if the model's predictions can only be calculated at a limited set
of model parameters. This uncertainty originates from using an emulator to
interpolate the model's prediction across a continuous space of parameters. In
this work, we study the trade-offs between the emulator (interpolation) and
statistical uncertainties. We perform the analysis using spatial eccentricities
from the T$_\mathrm{R}$ENTo model of initial conditions for nuclear collisions.
Given a fixed computational budget, we study the optimal compromise between the
number of parameter samples and the number of collisions simulated per
parameter sample. For the observables and parameters used in the present study,
we find that the best constraints are achieved when the number of parameter
samples is slightly smaller than the number of collisions simulated per
parameter sample.
