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Title: On a Dirichlet process mixture representation of phase-type distributions Authors:  Luis Gutierrez - Pontificia Universidad Catolica de Chile (Chile) [presenting]
Abstract: An explicit representation of phase-type distributions as an infinite mixture of Erlang distributions is introduced. The representation unveils a novel and helpful connection between a class of Bayesian nonparametric mixture models and phase-type distributions. Significantly, the connection sheds some light on two hot topics, estimation techniques for phase-type distributions and the availability of closed-form expressions for some functionals related to Dirichlet process mixture models. The power of this connection is illustrated via a posterior inference algorithm to estimate phase-type distributions, avoiding some difficulties with the simulation of latent Markov jump processes, commonly encountered in phase-type Bayesian inference. On the other hand, closed-form expressions for functionals of Dirichlet process mixture models are illustrated with density and renewal function estimation.