A Bayesian nonparametric model for density and cluster estimation: the ε -NGG process mixture Un modello bayesiano nonparametrico per la stima di densità e l’analisi di cluster: il modello mistura attraverso il processo ε -NGG

We define a new class of random probability measures, approximating the well-known normalized generalized gamma (NGG) process. Our new process is defined from the representation of NGG processes as discrete measures where the weights are obtained by normalization of the jumps of a Poisson process, and the support consists of iid points, however considering only jumps larger than a thresh- old ε . Therefore, the number of jumps of this new process, called ε -NGG process, is a.s. finite. A prior distribution for ε can be elicited. We will assume the ε -NGG process as the mixing measure in a mixture model for density and cluster estimation. Moreover, a efficient Gibbs sampler scheme to simulate from the posterior is provided. Finally, the performance of our algorithm on the Galaxy dataset will be illustrated.