Quasi-conjugate Bayes estimates for GPD parameters and application to heavy tails modelling

TL;DR

This paper introduces a quasi-conjugate Bayesian method for estimating GPD parameters, tail probabilities, and extreme quantiles, enhancing heavy tail modeling with credible interval assessments.

Contribution

It transfers Damsleth conjugate Bayes structure from Gamma to GPD, enabling efficient Gibbs sampling for parameter estimation and credible interval computation.

Findings

Bayes estimators perform comparably to standard methods on simulated data

The approach provides accurate credible intervals for extreme quantiles

Method effectively models heavy tails in real data sets

Abstract

We present a quasi-conjugate Bayes approach for estimating Generalized Pareto Distribution (GPD) parameters, distribution tails and extreme quantiles within the Peaks-Over-Threshold framework. Damsleth conjugate Bayes structure on Gamma distributions is transfered to GPD. Posterior estimates are then computed by Gibbs samplers with Hastings-Metropolis steps. Accurate Bayes credibility intervals are also defined, they provide assessment of the quality of the extreme events estimates. An empirical Bayesian method is used in this work, but the suggested approach could incorporate prior information. It is shown that the obtained quasi-conjugate Bayes estimators compare well with the GPD standard estimators when simulated and real data sets are studied.