- Bayesian Anal.
- Volume 3, Number 2 (2008), 367-391.
Bayesian nonparametrics for heavy tailed distribution. Application to food risk assessment
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.
Bayesian Anal., Volume 3, Number 2 (2008), 367-391.
First available in Project Euclid: 22 June 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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