B0349
Title: Mixture modeling via vector of normalized independent finite point processes
Authors: Alessandro Colombi - University of Milano-Bicocca (Italy) [presenting]
Raffaele Argiento - Università degli Studi di Bergamo (Italy)
Federico Camerlenghi - University of Milano-Bicocca (Italy)
Lucia Paci - Universita Cattolica del Sacro Cuore (Italy)
Abstract: During the last decade, the Bayesian nonparametric community has focused on the definition and investigation of prior distributions in the presence of hierarchical data. 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. In order to allow the borrowing of information across different groups, a random probability measure sharing the same atoms but with different weights is assumed. Theoretical properties of the model, such as predictive, posterior, and marginal distributions, are studied. The proposed random vector of probability measures is then used as a latent structure to define a group-dependent mixture model for clustering with a prior on the number of components. Inference is carried out through marginal and conditional Gibbs samplers. The method is motivated by clustering track and field athletes based on their average seasonal performance, treating performance measurements as random perturbations of an underlying individual step function with season-specific random intercepts. The prior is used to induce clustering of observations across seasons and athletes, identifying similarities and differences in performance by linking clusters across seasons. A real-world longitudinal shot put dataset is used to illustrate the proposed method.
