  Dirichlet process mixtures are particularly sensitive to the value of the
so-called precision parameter, which controls the behavior of the underlying
latent partition. Randomization of the precision through a prior distribution
is a common solution, which leads to more robust inferential procedures.
However, existing prior choices do not allow for transparent elicitation, due
to the lack of analytical results. We introduce and investigate a novel prior
for the Dirichlet process precision, the Stirling-gamma distribution. We study
the distributional properties of the induced random partition, with an emphasis
on the number of clusters. Our theoretical investigation clarifies the reasons
of the improved robustness properties of the proposed prior. Moreover, we show
that, under specific choices of its hyperparameters, the Stirling-gamma
distribution is conjugate to the random partition of a Dirichlet process. We
illustrate with an ecological application the usefulness of our approach for
the detection of communities of ant workers.
