European Institute for Statistics, Probability, Stochastic Operations Research
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Bayesian nonparametric inference for discovery probabilities: credible intervals and large sample asymptotics
Julyen Arbel, Inria Grenoble Rhône-Alpes

Given a sample of size n from a population of individual belonging to different species with unknown proportions, a popular problem of practical interest consists in making inference on the probability D_n(l) that the (n+1)-th draw coincides with a species with frequency l in the sample, for any l=0,1,...,n. We explore in this talk a Bayesian nonparametric viewpoint for inference of D_n(l). Specifically, under the general framework of Gibbs-type priors we show how to derive credible intervals for the Bayesian nonparametric estimator of D_n(l), and we investigate the large n asymptotic behavior of such an estimator. We also compare this estimator to the classical Good–Turing estimator (joint work with Stefano Favaro (Collegio Carlo Alberto & University of Torino), Bernardo Nipoti (Trinity College Dublin) and Yee Whye Teh (Oxford University)).

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