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Title: Bayesian sensitivity analysis of the parameters of a GPD using distorted band classes Authors:  Jose Pablo Arias-Nicolas - University of Extremadura (Spain) [presenting]
Alfonso Suarez-Llorens - Universidad de Cadiz (Spain)
Abstract: The objective of extreme value analysis is to model and measure tail events that occur with small probability, using only extreme values above some high threshold rather than using all of the data. It is well known that, for high thresholds, the excess distribution function can be approximated by a Generalized Pareto Distribution (GPD), which is used as much more reliable than the normal distribution due to the fact that gives the accent on the extreme values. Two measures that we find most useful and reliable for describing the tail of the distribution are value-at-risk and expected shortfall. Robust Bayesian analysis, also called Bayesian sensitivity analysis, aims to quantify and interpret the uncertainty induced by the partial knowledge of one of the three elements in Bayesian analysis (prior, likelihood and loss). Studies mainly focus on computing the range of some quantities of interest when the prior distribution varies in a class. We use the band distorted class to compute the range of the parameters of a Generalized Pareto Distribution. The two risk measures, value-at-risk and expected shortfall, are constructed based on the Bayesian estimation results.