Statistical Modelling 11 (2011), 557–580

A default Bayesian approach for regression on extremes

Stefano Cabras
Department of Mathematics,
University of Cagliari
via Ospedale 72
I–09124 Cagliari
Italy
eMail: s.cabras@unica.it

María Eugenia Castellanos
Department of Statistics and Operation Research,
Rey Juan Carlos University
Spain

Dani Gamerman
Institute of Mathematics,
Universidade Federal do Rio de Janeiro
Brazil

Abstract:

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.

Keywords:

extreme values; Jeffreys’ prior; K-year return level; non-homogenous Poisson-GPD; Peaks Over the Threshold

Downloads:

Appendix

Example data and R code in zipped archive


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