A0401
Title: Mixture modeling via vectors of normalized independent finite point processes
Authors: Federico Camerlenghi - University of Milano-Bicocca (Italy) [presenting]
Alessandro Colombi - University of Milano-Bicocca (Italy)
Lucia Paci - Universita Cattolica del Sacro Cuore (Italy)
Raffaele Argiento - Università degli Studi di Bergamo (Italy)
Abstract: During the last decade, the Bayesian nonparametric community has focused on the definition and investigation of prior distributions in presence of multiple-sample information. A large variety of available models are typically defined by relying on suitable transformations of infinite point processes. Here we define a vector of dependent random probability measures for data organized in groups by normalizing a class of dependent finite point processes. In order to allow the borrowing of information across the diverse groups, we assume that the random probability measures share the same atoms but with different weights. We are able to study all the theoretical properties of the model, 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. We develop both marginal and conditional algorithms to carry out posterior inference. The performance of the model is tested on several simulated scenarios, and the method is applied to cluster track and field athletes based on their average seasonal performance.
