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.
Type de document :
Communication dans un congrès
Mathematical Methods of Modern Statistics, Jul 2017, Marseille, France. 〈http://scientific-events.weebly.com/1487.html〉
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https://hal.archives-ouvertes.fr/hal-01667765
Contributeur : Julyan Arbel <>
Soumis le : mardi 19 décembre 2017 - 15:37:10
Dernière modification le : mercredi 11 avril 2018 - 01:59:18

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  • HAL Id : hal-01667765, version 1

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Julyan Arbel. Investigating predictive probabilities of Gibbs-type priors. Mathematical Methods of Modern Statistics, Jul 2017, Marseille, France. 〈http://scientific-events.weebly.com/1487.html〉. 〈hal-01667765〉

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