Title: Bayesian sensitivity analysis of posterior predictive distribution in extreme value theory
Authors: Jose Pablo Arias-Nicolas - University of Extremadura (Spain) [presenting]
Eva Lopez Sanjuan - Universidad de Extremadura (Spain)
M Isabel Parra Arevalo - Universidad de Extremadura (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 the data. It is well known that, when we consider the values of the sample space above a certain value (threshold) the limit distribution function is a Generalized Pareto Distribution. Two measures that we find most useful and reliable for describing the tail of the distribution are Value at risk (VaR) and expected shortfall (ES). Under a Bayesian framework, we use the band distorted class to compute the range of these two risk measures for the posterior predictive density. The most important property is that the likelihood ratio order we are using in this class is preserved after the application the posterior belief. In the same way, we can see something similar for predictive distributions. We show that computations of sensitivity measures should be as easy as possible, possibly looking for the extremal distributions generating the class. Due to the fact that the distorted band depends on the election of the reference prior distribution (also on the distorted functions considered), we illustrate with some numerical examples, how this choice affects the calculation of the measures considered. Moreover, we compare the results considering the data from some standard populations: Normal, Exponential, Cauchy,...