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Title: A conjugate prior for the Dirichlet process precision parameter Authors:  Tommaso Rigon - University of Milano-Bicocca (Italy) [presenting]
Alessandro Zito - Duke University (United States)
David Dunson - Duke University (United States)
Abstract: A new prior distribution is presented for the precision parameter of a Dirichlet process. We show how this prior is conjugate to the distribution of the number of distinct values arising from the process. Moments, properties and hyperparameters interpretation of the distribution are extensively studied, as well as its relationship with the class of exponential families. Interestingly, certain choices for the hyperparameters allow to compute the normalizing constant explicitly. We show how this allows to draw a parallel with common Bayesian nonparametric models within the class of Gibbs-type processes. We illustrate practical advantages of using this prior over common alternatives proposed in the literature when adopting a Dirichlet process-based clustering algorithm.