  Cluster analysis aims at partitioning data into groups or clusters. In
applications, it is common to deal with problems where the number of clusters
is unknown. Bayesian mixture models employed in such applications usually
specify a flexible prior that takes into account the uncertainty with respect
to the number of clusters. However, a major empirical challenge involving the
use of these models is in the characterisation of the induced prior on the
partitions. This work introduces an approach to compute descriptive statistics
of the prior on the partitions for three selected Bayesian mixture models
developed in the areas of Bayesian finite mixtures and Bayesian nonparametrics.
The proposed methodology involves computationally efficient enumeration of the
prior on the number of clusters in-sample (termed as ``data clusters'') and
determining the first two prior moments of symmetric additive statistics
characterising the partitions. The accompanying reference implementation is
made available in the R package 'fipp'. Finally, we illustrate the proposed
methodology through comparisons and also discuss the implications for prior
elicitation in applications.
