# Investigating predictive probabilities of Gibbs-type priors

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.
Document type :
Conference papers
Domain :

https://hal.archives-ouvertes.fr/hal-01667765
Contributor : Julyan Arbel <>
Submitted on : Tuesday, December 19, 2017 - 3:37:10 PM
Last modification on : Tuesday, May 11, 2021 - 11:37:37 AM

### Identifiers

• HAL Id : hal-01667765, version 1

### Citation

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

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