Approximating 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
ERCIM - 10th International Conference of the ERCIM WG on Computational and Methodological Statistics, Dec 2017, London, United Kingdom. 2017, 〈http://cmstatistics.org/CMStatistics2017/〉
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https://hal.archives-ouvertes.fr/hal-01667746
Contributeur : Julyan Arbel <>
Soumis le : mardi 19 décembre 2017 - 15:29:51
Dernière modification le : jeudi 11 janvier 2018 - 01:48:44

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  • HAL Id : hal-01667746, version 1

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Julyan Arbel. Approximating predictive probabilities of Gibbs-type priors. ERCIM - 10th International Conference of the ERCIM WG on Computational and Methodological Statistics, Dec 2017, London, United Kingdom. 2017, 〈http://cmstatistics.org/CMStatistics2017/〉. 〈hal-01667746〉

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