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Title: Stick-breaking processes with exchangeable length variables Authors:  Maria Fernanda Gil-Leyva Villa - IIMAS,UNAM (Mexico) [presenting]
Ramses Mena - UNAM (Mexico)
Abstract: The stick-breaking construction is a well-known method to define distributions on the infinite-dimensional simplex as well as Bayesian nonparametric priors. Due to the mathematical hurdles to overcome, most efforts of studying this class with some generality, have concentrated in the case where the underlying length variables are independent. The focus is on the general class of stick-breaking processes with exchangeable length variables. These generalize well-known Bayesian non-parametric priors, such as Dirichlet and Geometric processes, in an unexplored direction. We give conditions to assure the respective species sampling process is discrete almost surely and the corresponding prior has full support. For a rich sub-class, we study the ordering of the stick-breaking weights and derive and an MCMC algorithm for density estimation purposes.