A0882
Title: Bayesian nonparametric modelling of latent partitions via Stirling-gamma priors
Authors: Alessandro Zito - Duke University (United States) [presenting]
Tommaso Rigon - University of Milano-Bicocca (Italy)
David Dunson - Duke University (United States)
Abstract: The Dirichlet process (DP) has received much attention in recent decades as an effective tool for clustering and density estimation. However, DP mixtures are particularly sensitive to the value of the precision parameter, which must be chosen carefully to prevent over-clustering. Moreover, common choices of priors for the precision, such as the gamma distribution, induce an analytically intractable prior over the associated number of clusters. A class of priors is introduced for the precision parameter that instead makes the induced prior over the number of clusters tractable and approximately distributed as a Negative Binomial. The prior belongs to the novel class of Stirling-gamma distributions, which are flexible and easily sampled from. It has been shown how certain choices of the hyperparameters of the Stirling-gamma allow obtaining conjugacy to the law of the random partition generated by a DP and the number of associated clusters therein. This leads to a very interpretable prior specification, simplifying both prior elicitation and posterior computations. The resulting marginal process is framed within the larger class of Gibbs-type partition models. The conjugate case also shows how the Stirling-gamma allows for the borrowing of information across multiple observed partitions.
