Investigating predictive probabilities of Gibbs-type priors

Julyan Arbel 1
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : Gibbs-type priors are arguably the most 'natural' generalization of the Dirichlet prior. Among them the two parameter Poisson-Dirichlet prior certainly stands out for the simplicity and intuitiveness of its predictive probabilities. Given an observable sample of size $n$, in this paper we show that the predictive probabilities of any Gibbs-type prior admit a large $n$ approximation, with an error term vanishing as $o(1/n)$, which maintains the same mathematical tractability and interpretability as the predictive probabilities of the two parameter Poisson-Dirichlet prior. We discuss the use of our approximate predictive probabilities in connection with some recent work on Bayesian nonparametric inference for discovery probabilities.
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Contributor : Julyan Arbel <>
Submitted on : Tuesday, December 19, 2017 - 3:37:10 PM
Last modification on : Wednesday, April 11, 2018 - 1:59:18 AM

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Julyan Arbel. Investigating predictive probabilities of Gibbs-type priors. Mathematical Methods of Modern Statistics, Jul 2017, Marseille, France. ⟨hal-01667765⟩

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