  Gravitational waves (GWs) have revealed surprising properties of binary black
hole (BBH) populations, but there is still mystery surrounding how these
compact objects evolve. We apply Bayesian inference and an efficient method to
calculate the BBH merger rates in the Shark host galaxies, to determine the
combination of COMPAS parameters that outputs a population most like the GW
sources from the LVK transient catalogue. For our COMPAS models, we calculate
the likelihood with and without the dependence on the predicted number of BBH
merger events. We find strong correlations between hyper-parameters governing
the specific angular momentum (AM) of mass lost during mass transfer, the
mass-loss rates of Wolf--Rayet stars via winds and the chemically homogeneous
evolution (CHE) formation channel. We conclude that analysing the marginalised
and unmarginalised likelihood is a good indicator of whether the population
parameters distribution and number of observed events reflect the LVK data. In
doing so, we see that the majority of the models preferred in terms of the
population-level parameters of the BBHs greatly overpredict the number of
events we should have observed to date. Looking at the smaller number of models
which perform well with both likelihoods, we find that those with no CHE, AM
loss occurring closer to the donor during the first mass-transfer event, and/or
higher rates of mass-loss from Wolf--Rayet winds are generally preferred by
current data. We find these conclusions to be robust to our choice of selection
criteria.
