A0486
Title: Dependent nonparametric priors based on finite point processes
Authors: Alessandro Colombi - University of Milano-Bicocca (Italy)
Raffaele Argiento - Università degli Studi di Bergamo (Italy)
Federico Camerlenghi - University of Milano-Bicocca (Italy) [presenting]
Lucia Paci - Universita Cattolica del Sacro Cuore (Italy)
Abstract: During the last decade, the Bayesian nonparametric community has focused on defining and investigating prior distributions in the presence of multiple-sample information. A large variety of available models are typically defined by relying on suitable transformations of infinite point processes. A vector of dependent random probability measures is defined for data organized in groups by normalizing a class of dependent finite point processes. It is assumed that the random probability measures to share the same atoms but with different weights to allow the borrowing of information across diverse groups. The model's theoretical properties are studied, i.e., the predictive, posterior and marginal distributions. The random vector of probability measures we propose is then used as a latent structure to define a level-dependent mixture model for clustering with a prior on the number of components. The usefulness of our proposal is also showcased to address extrapolation problems in the presence of multiple populations of species with unknown proportions. In such a setting, closed-form expressions are derived for many statistics of interest, which are still missing in the species literature.
