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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, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, LJK - Laboratoire Jean Kuntzmann
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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https://hal.archives-ouvertes.fr/hal-01667746
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Submitted on : Tuesday, December 19, 2017 - 3:29:51 PM
Last modification on : Friday, February 4, 2022 - 3:22:50 AM

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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. ⟨hal-01667746⟩

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