A1045
Title: Bayesian mixture models with repulsive and attractive atoms
Authors: Alessandra Guglielmi - Politecnico di Milano (Italy) [presenting]
Abstract: The study of almost surely discrete random probability measures is an active line of research in Bayesian non-parametrics. The idea of assuming interaction across the atoms of the random probability measure has recently spurred significant interest in the context of Bayesian mixture models. This allows the definition of priors that encourage well-separated and interpretable clusters. A unified framework is provided for the construction and the Bayesian analysis of random probability measures with interacting atoms, encompassing both repulsive and attractive behaviours. Specifically, closed-form expressions are derived for the posterior distribution, the marginal and predictive distributions, previously unavailable except for the case of measures with i.i.d. atoms. It is shown how these quantities are fundamental for both prior elicitation and developing new posterior simulation algorithms for hierarchical mixture models. Results are obtained without any assumption on the finite point process governing the atoms of the random measure. The treatment is specialized to the classes of Poisson, Gibbs, and determinantal point processes, as well as in the case of shot-noise Cox processes. Finally, the modelling strategies are seen on simulated and real datasets.
