Title: Compositions of discrete random probabilities for inference on multiple samples
Authors: Giovanni Rebaudo - University of Texas at Austin (United States) [presenting]
Augusto Fasano - Collegio Carlo Alberto and European Commission - Joint Research Centre (Italy)
Antonio Lijoi - Bocconi University (Italy)
Igor Pruenster - Bocconi University (Italy)
Abstract: Bayesian hierarchical models have proved to be an effective tool when observations are from different populations or studies, since they naturally allow borrowing information across groups, while allowing the subjects in the same group to share the same unknown distribution. We consider models induced by compositions of discrete random probabilities measures, most notably Pitman-Yor processes. Such compositions are well suited to account for both clustering of populations and clustering of observations. We identify an analytical expression of the distribution of the induced random partition, and this allows us to gain a deeper insight into the theoretical properties of the model while deriving predictive distributions and urn schemes. The proposed models can be used as a building block for addressing problems of density estimation, prediction with species sampling data and testing of distributional homogeneity. The theoretical results further lead us to devise novel MCMC sampling schemes whose effectiveness will be discussed through illustrative examples involving simulated and real data.