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hal-00184755, version 2

Bayesian Nonparametrics for Heavy Tailed Distribution Application to Food Risk Assessment

Jessica Tressou () 12

Bayesian Analysis 3, 2 (2008) 367-392

Résumé : Using the fact that any heavy tailed distribution can be approximated by a, possibly in...nite, mixture of Pareto distributions, this paper proposes two Bayesian methodologies tailored to infer on distribution tails belonging to the Fréchet domain of attraction. Firstly, a Bayesian Pareto based clustering procedure is developed, where the mixing distribution is chosen to be the classical conjugate prior of the Pareto distribution. It allows one to group n objects into a certain number of clusters according to their extremal behavior. It also exhibits a new estimator for the tail index. Secondly a nonparametric extension of the model based clustering is proposed in which the parameter of interest is the mixing distribution. Estimation of the tail probability is conducted using a Dirichlet process prior for the unknown mixing distribution. As an illustration, both methodologies are applied to simulated data sets and a true data set concerning dietary exposure to a mycotoxin called Ochratoxin A.

  • 1 :  Méthodologies d'Analyse de Risque Alimentaire (MET@RISK)
  • Institut national de la recherche agronomique (INRA) : UR1204
  • 2 :  Hong Kong University of Science and Technology - Information Systems, Business Statistics & Operations Management (HKUST-ISMT)
  • Hong Kong University of Science and Technology
  • Domaine : Mathématiques/Statistiques
    Statistiques/Théorie
  • Mots-clés : Dirichlet process – Model Based clustering – Ochratoxin A – Tail index estimation
  • Versions disponibles :  v1 (01-11-2007) v2 (27-03-2008)
 
  • hal-00184755, version 2
  • oai:hal.archives-ouvertes.fr:hal-00184755
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  • Soumis le : Jeudi 27 Mars 2008, 09:48:27
  • Dernière modification le : Jeudi 13 Septembre 2012, 17:56:37