Bayesian Nonparametrics for Heavy Tailed Distribution Application to Food Risk Assessment

Jessica Tressou (1, 2)

1 MET@RISK - Méthodologies d'Analyse de Risque Alimentaire
2 HKUST-ISMT - Hong Kong University of Science and Technology - Information Systems, Business Statistics & Operations Management

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.

Mots clés: Dirichlet process; Model Based clustering; Ochratoxin A; Tail index estimation

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jessica Tressou. Bayesian Nonparametrics for Heavy Tailed Distribution Application to Food Risk Assessment. Bayesian Analysis, 2008, 3 (2), pp.367-392. ⟨10.1214/08-BA314⟩. ⟨hal-00184755v2⟩