Regression models to dependence for exceedance

Abstract

Extreme Value Theory (EVT) aims to study the tails of probability distributions in order to measure and quantify extreme events of maximum and minimum. In river flow data, an extreme level of a river may be related to the level of a neighboring river that flows into it. In this type of data, it is very common for flooding of a location to have been caused by a very large flow from an affluent river that is tens or hundreds of kilometers from this location. In this sense, an interesting approach is to consider a conditional model for the estimation of a multivariate model. Inspired by this idea, we propose a Bayesian model to describe the dependence of exceedance between rivers, where we considered a conditionally independent structure. In this model, the dependence between rivers is captured by modeling the excess marginally of one river as a consequence of linear functions of the other rivers. The results showed that there is a strong and positive connection between excesses in one river caused by the excesses of the other rivers.