Title: Importance conditional sampler for Bayesian nonparametric mixtures
Authors: Riccardo Corradin - University of Milano Bicocca (Italy) [presenting]
Bernardo Nipoti - University of Milan Bicocca (Italy)
Antonio Canale - University of Padua (Italy)
Abstract: Bayesian nonparametric mixtures are flexible models for density estimation and model based clustering, nowadays a common tool for the applied statisticians. In this family of models, Pitman-Yor mixtures show a good balance between mathematical tractability and flexibility. Inference for this class of models is mainly performed by means of MCMC methods, which can be divided into marginal and conditional methods. Marginal methods are easily interpretable, although they underestimate the uncertainty associated to posterior quantities. On the other hand, conditional methods provide an accurate estimation of posterior uncertainty. We recently introduced a sampling strategy to estimate Pitman-Yor mixtures, named importance conditional sampler (ICS). Our proposal has proved to be highly efficient and robust to the specification of the parameters characterising the distribution of the underlying process. The ICS provides an accurate estimation of posterior uncertainty, and, like marginal methods, it is described by a simple and interpretable predictive structure. Motivated by an astronomical application, we extended the ICS approach to Griffiths-Milne dependent mixtures, a family of models for partially exchangeable data.