A Semiparametric Bayesian Approach for Extreme Values Using Dirichlet Process Mixture of Gamma and Generalized Pareto Densities

TL;DR

This paper introduces a Bayesian semiparametric model combining Dirichlet process mixtures of gamma and generalized Pareto densities for flexible extreme value estimation, suitable for data without prior information.

Contribution

It presents a novel, easy-to-implement Bayesian approach for modeling extremes using a mixture model that adapts to data without prior assumptions.

Findings

Effective in estimating high quantiles in simulated data

Applicable to real-world datasets with good performance

Provides a sensitivity analysis for model robustness

Abstract

For extreme value estimation we propose to use a model with a Dirichlet process mixture of gamma densities in the center and generalized Pareto densities for the tails. Due to the randomness in the center and a heavy tailed density in the tails density estimation and posterior inference for high quantiles are possible. The approach can be used in a "default" manner on the positive reals because it works when prior information is unavailable. The proposed model can be easy to implement and a sensitivity analysis is provided. We applied the proposed model for simulated and real data sets.