Bayesian nonparametric inference for discovery probabilities: credible intervals and large sample asymptotics

Abstract : Given a sample of size n from a population of individual belonging to different species with unknown proportions, a popular problem of practical interest consists in making inference on the probability Dn(l) that the (n+1)-th draw coincides with a species with frequency l in the sample, for any l=0,1,…,n. This paper contributes to the methodology of Bayesian nonparametric inference for Dn(l). Specifically, under the general framework of Gibbs-type priors we show how to derive credible intervals for the Bayesian nonparametric estimator of Dn(l), and we investigate the large n asymptotic behaviour of such an estimator. Of particular interest are special cases of our results obtained under the assumption of the two parameter Poisson-Dirichlet prior and the normalized generalized Gamma prior, which are two of the most commonly used Gibbs-type priors. With respect to these two prior assumptions, the proposed results are illustrated through a simulation study and a benchmark Expressed Sequence Tags dataset. To the best our knowledge, this illustration provides the first comparative study between the two parameter Poisson-Dirichlet prior and the normalized generalized Gamma prior in the context of Bayesian nonparemetric inference for Dn(l)
Type de document :
Article dans une revue
Statistica Sinica, Taipei : Institute of Statistical Science, Academia Sinica, 2017, 27, pp.839-858. 〈http://www3.stat.sinica.edu.tw/statistica/J27N2/J27N218/J27N218.html〉. 〈10.5705/ss.202015.0250〉
Liste complète des métadonnées

Littérature citée [40 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01203324
Contributeur : Julyan Arbel <>
Soumis le : jeudi 24 septembre 2015 - 16:48:23
Dernière modification le : vendredi 19 octobre 2018 - 11:28:03
Document(s) archivé(s) le : mardi 29 décembre 2015 - 09:22:08

Fichier

discovery.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Julyan Arbel, Stefano Favaro, Bernardo Nipoti, Yee Whye Teh. Bayesian nonparametric inference for discovery probabilities: credible intervals and large sample asymptotics. Statistica Sinica, Taipei : Institute of Statistical Science, Academia Sinica, 2017, 27, pp.839-858. 〈http://www3.stat.sinica.edu.tw/statistica/J27N2/J27N218/J27N218.html〉. 〈10.5705/ss.202015.0250〉. 〈hal-01203324〉

Partager

Métriques

Consultations de la notice

301

Téléchargements de fichiers

80