  Monte Carlo simulations are widely used in nuclear physics to model
experimental systems. In cases where there are significant unknown quantities,
such as energies of states, an iterative process of simulating and fitting is
often required to describe experimental data. We describe a Bayesian approach
to fitting experimental data, designed for data from a $^{12}$Be(d,p) reaction
measurement, using simulations made with GEANT4. Q-values from the
$^{12}$C(d,p) reaction to well-known states in $^{13}$C are compared with
simulations using BayesOpt. The energies of the states were not included in the
simulation to reproduce the situation for $^{13}$Be where the states are poorly
known. Both cases had low statistics and significant resolution broadening
owing to large proton energy losses in the solid deuterium target. Excitation
energies of the lowest three excited states in $^{13}$C were extracted to
better than 90 keV, paving a way for extracting information on $^{13}$Be.
