On selecting a prior for the precision parameter of Dirichlet process mixture models

In hierarchical mixture models the Dirichlet process is used to specify latent patterns of heterogeneity, particularly when the distribution of latent parameters is thought to be clustered (multimodal). The parameters of a Dirichlet process include a precision parameter αα and a base probability measure G0G0. In problems where αα is unknown and must be estimated, inferences about the level of clustering can be sensitive to the choice of prior assumed for αα. In this paper an approach is developed for computing a prior for the precision parameter αα that can be used in the presence or absence of prior information about the level of clustering. This approach is illustrated in an analysis of counts of stream fishes. The results of this fully Bayesian analysis are compared with an empirical Bayes analysis of the same data and with a Bayesian analysis based on an alternative commonly used prior.