Title: On the Pitman-Yor process with spike and slab prior specification
Authors: Bernardo Nipoti - University of Milan Bicocca (Italy) [presenting]
Igor Pruenster - Bocconi University (Italy)
Antonio Lijoi - University of Pavia and Collegio Carlo Alberto (Italy)
Antonio Canale - University of Padua (Italy)
Abstract: For the most popular discrete nonparametric models, beyond the Dirichlet process, the prior guess at the shape of the data generating distribution, also known as base measure, is assumed to be diffuse. Such a specification greatly simplifies the derivation of analytical results allowing for a straightforward implementation of Bayesian nonparametric inferential procedures. However, in several applied problems the available prior information leads naturally to incorporate an atom into the base measure and one is essentially left with the Dirichlet process as the only tractable choice for the prior. We fill this gap by considering the Pitman-Yor process featuring an atom in its base measure. We derive computable expressions for the distribution of the induced random partitions and for the predictive distributions. These findings allow us to devise an effective generalized Polya urn Gibbs sampler. Applications to density estimation, clustering and curve estimation, with both simulated and real data, serve as an illustration of our results and allow comparisons with existing methodology. In particular, we tackle a functional data analysis problem concerning basal body temperature curves.