On the Jeffreys prior for the multivariate Ewens distribution

We derive the Jeffreys prior for the parameter of the Multivariate Ewens Distribution and study some of its properties. In particular, we show that this prior is proper and has no finite moments. We also investigate the impact of this prior on the a priori distribution of the number of species and the a priori probability of discovery of a new species, which are usually employed in subjective prior elicitation. The effect of the Jeffreys prior for posterior inference is illustrated using examples arising in the context of inference for species sampling models and Dirichlet process mixture models.