  In model-based clustering, the Galaxy data set is often used as a benchmark
data set to study the performance of different modeling approaches. Aitkin
(2001) compares maximum likelihood and Bayesian analyses of the Galaxy data set
and expresses reservations about the Bayesian approach due to the fact that the
prior assumptions imposed remain rather obscure while playing a major role in
the results obtained and conclusions drawn.
  The aim of the paper is to address Aitkin's concerns about the Bayesian
approach by shedding light on how the specified priors influence the number of
estimated clusters. We perform a sensitivity analysis of different prior
specifications for the mixtures of finite mixture model, i.e., the mixture
model where a prior on the number of components is included. We use an
extensive set of different prior specifications in a full factorial design and
assess their impact on the estimated number of clusters for the Galaxy data
set. Results highlight the interaction effects of the prior specifications and
provide insights into which prior specifications are recommended to obtain a
sparse clustering solution. A simulation study with artificial data provides
further empirical evidence to support the recommendations.
  A clear understanding of the impact of the prior specifications removes
restraints preventing the use of Bayesian methods due to the complexity of
selecting suitable priors. Also, the regularizing properties of the priors may
be intentionally exploited to obtain a suitable clustering solution meeting
prior expectations and needs of the application.
