Default Bayesian Analysis for the Multivariate Ewens Distribution

TL;DR

This paper derives and analyzes the Jeffreys prior for the Multivariate Ewens Distribution, examining its properties and impact on species sampling inference, with applications to Dirichlet process models.

Contribution

It introduces the Jeffreys prior for the Multivariate Ewens Distribution and studies its properties and implications for species sampling and Bayesian inference.

Findings

The Jeffreys prior is proper but has no finite moments.

It influences the prior distribution of the number of species and discovery probability.

Applications demonstrate its effect on posterior inference in species sampling models.

Abstract

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 default 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.