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Rates of convergence for the posterior distributions of mixtures of Betas and adaptive nonparametric estimation of the density
Annals of Statistics
In this paper, we investigate the asymptotic properties of nonparametric Bayesian mixtures of Betas for estimating a smooth density on [0,1]. We consider a parametrization of Beta distributions in terms of mean and scale parameters and construct a mixture of these Betas in the mean parameter, while putting a prior on this scaling parameter. We prove that such Bayesian nonparametric models have good frequentist asymptotic properties. We determine the posterior rate of concentration around thedoi:10.1214/09-aos703 fatcat:mtaapelqzrb7nkg6iabmobw3ky