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Non‐parametric Bayesian inference on bivariate extremes
Author(s) -
Guillotte Simon,
Perron François,
Segers Johan
Publication year - 2011
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2010.00770.x
Subject(s) - mathematics , frequentist inference , markov chain monte carlo , measure (data warehouse) , bayesian probability , estimator , extreme value theory , bayesian inference , statistics , computer science , database
Summary. The tail of a bivariate distribution function in the domain of attraction of a bivariate extreme value distribution may be approximated by that of its extreme value attractor. The extreme value attractor has margins that belong to a three‐parameter family and a dependence structure which is characterized by a probability measure on the unit interval with mean equal to , which is called the spectral measure. Inference is done in a Bayesian framework using a censored likelihood approach. A prior distribution is constructed on an infinite dimensional model for this measure, the model being at the same time dense and computationally manageable. A trans‐dimensional Markov chain Monte Carlo algorithm is developed and convergence to the posterior distribution is established. In simulations, the Bayes estimator for the spectral measure is shown to compare favourably with frequentist non‐parametric estimators. An application to a data set of Danish fire insurance claims is provided.