Selecting the precision parameter prior in Dirichlet process mixture models

We consider Dirichlet process mixture models in which the observed clusters in any particular dataset are not viewed as belonging to a finite set of possible clusters but rather as representatives of a latent structure in which objects belong to one of a potentially infinite number of clusters. As more information is revealed the number of inferred clusters is allowed to grow. The precision parameter of the Dirichlet process is a crucial parameter that controls the number of clusters. We develop a framework for the specification of the hyperparameters associated with the prior for the precision parameter that can be used both in the presence or absence of subjective prior information about the level of clustering. Our approach is illustrated in an analysis of clustering brands at the magazine Which?. The results are compared with the approach of Dorazio (2009) via a simulation study.