  Bayesian analysis methods often use some form of iterative simulation such as
Monte Carlo computation. Models that involve discrete variables can sometime
pose a challenge, either because the methods used do not support such variables
(e.g. Hamiltonian Monte Carlo) or because the presence of such variables can
slow down the computation. A common workaround is to marginalise the discrete
variables out of the model. While it is reasonable to expect that such
marginalisation would also lead to more time-efficient computations, to our
knowledge this has not been demonstrated beyond a few specialised models.
  We explored the impact of marginalisation on the computational efficiency for
a few simple statistical models. Specifically, we considered two- and
three-component Gaussian mixture models, and also the Dawid-Skene model for
categorical ratings. We explored each with two software implementations of
Markov chain Monte Carlo techniques: JAGS and Stan. We directly compared
marginalised and non-marginalised versions of the same model using the samplers
on the same software.
  Our results show that marginalisation on its own does not necessarily boost
performance. Nevertheless, the best performance was usually achieved with Stan,
which requires marginalisation. We conclude that there is no simple answer to
whether or not marginalisation is helpful. It is not necessarily the case that,
when turned 'on', this technique can be assured to provide computational
benefit independent of other factors, nor is it likely to be the model
component that has the largest impact on computational efficiency.
