Bayesian Analysis

Bayesian nonparametrics for heavy tailed distribution. Application to food risk assessment

Jessica Tressou

Full-text: Open access

Abstract

Based on the fact that any heavy tailed distribution can be approximated by a possibly infinite mixture of Pareto distributions, this paper proposes two Bayesian methodologies tailored to infer on distribution tails belonging to the Frèchet 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. This allows the grouping of $n$ objects into a certain number of clusters according to their extremal behavior and 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. To illustrate, both methodologies are applied to simulated data sets and a real data set concerning dietary exposure to a mycotoxin called Ochratoxin A.

Article information

Source
Bayesian Anal., Volume 3, Number 2 (2008), 367-391.

Dates
First available in Project Euclid: 22 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ba/1340370552

Digital Object Identifier
doi:10.1214/08-BA314

Mathematical Reviews number (MathSciNet)
MR2407431

Zentralblatt MATH identifier
1330.62183

Keywords
Dirichlet process Model Based clustering Ochratoxin A Tail index estimation

Citation

Tressou, Jessica. Bayesian nonparametrics for heavy tailed distribution. Application to food risk assessment. Bayesian Anal. 3 (2008), no. 2, 367--391. doi:10.1214/08-BA314. https://projecteuclid.org/euclid.ba/1340370552


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