A Bayesian semi-parametric approach to extreme regime identification

Limiting tail behavior of distributions are known to follow one of three possible limiting distributions, depending on the domain of attraction of the observational model under suitable regularity conditions. This work proposes a new approach for identification and analysis of the limiting regimes that these data exceedances belong to. The model-based approach uses a mixture at the observational level where a Generalized Pareto distribution (GPD) is assumed above the threshold. The novelty of this work is the study of the behavior of the GPD through another mixture distribution over the three possible regimes. Adequate solution to this evaluation is shown to require a mixed prior distribution with a point mass, unlike previous work in the area. In some applications, estimation results showed one regime is clearly indicated by the data whereas in other applications there is no clear indication of the regime. This estimation is based on evaluation of posterior probabilities for each regime. Simulation exercises were conducted to evaluate the accuracy of the model in various parameter settings and sample sizes, specifically in the estimation of high quantiles. They show an improved performance over existing approaches. Results of environmental applications show that the point mass approach plays a vital role in this study. Key-Words: Extreme value theory, GPD distribution, environmental data, MCMC, Bayesian Inference.