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B0602
Title: Model-based clustering via normalized completely random measure mixtures Authors:  Raffaele Argiento - Università degli Studi di Bergamo (Italy) [presenting]
Alessandra Guglielmi - Politecnico di Milano (Italy)
Ilaria Bianchini - Politecnico di Milano (Italy)
Abstract: Mixtures of parametric densities arise as the natural statistical tool when dealing with model-based clustering problems, and a very flexible class of such mixtures is obtained when the mixing measure is a random probability measure, possibly a.s. discrete. We consider mixtures when the mixing probability measure is within a large class of random probability measures, that is normalized completely random measures (NCRM). However, the computational effort to compute the relevant posteriors in this case can be very burdensome, since MCMC schemes are complicated by the presence of an infinite number of parameters. We propose a truncation method to approximate the mixing measure and simplify the computations. Since a NCRM is a random discrete measure where the weights are obtained by normalization of the points of a Poisson process, we discard those larger than a threshold epsilon. Hence, the number of parameters becomes finite, so that an efficient blocked Gibbs sampler to simulate from the posterior is built. To show the performance of our algorithm and the flexibility of the model, we will illustrate two example via NCRM mixtures: the first consider a new NCRM called Bessel random probability measure as the mixing measure, and then apply the mixture to simulated and a real dataset, while the second deals with a linear dependent epsilon-NGG mixture to fit a well known dataset.