A default Bayesian approach for regression on extremes

A default Bayesian approach to predict extreme events in the presence of explanatory variables is presented. In the prediction model, covariates are introduced, using a non-homogenous Poisson-Generalized Pareto Distribution (GPD) point process, which allows for variation in the tail behaviour. The prior distribution proposed is based on a Jeffreys’ rule for regression parameters, extending the results previously obtained for an independent and identically distributed random sample drawn from the GPD. Special attention is given to mean return levels as an important summarizer. Inference is performed approximately via Markov chain Monte Carlo methods and the posterior distribution turns out to be relatively easy to be computed. The model is applied to two real datasets from meteorological applications