A Semiparametric Bayesian Extreme Value Model Using a Dirichlet Process Mixture of Gamma Densities

TL;DR

This paper introduces a flexible semiparametric Bayesian model combining Dirichlet process mixtures of gamma densities for the bulk and a generalized Pareto for the tail, enabling effective extreme value estimation even with limited data.

Contribution

It presents a novel semiparametric Bayesian approach using Dirichlet process mixtures for modeling extremes, improving inference for small samples and minimal prior information.

Findings

Model performs well in simulations

Accurate estimation of high quantiles

Effective for small sample sizes

Abstract

In this paper we propose a model with a Dirichlet process mixture of gamma densities in the bulk part below threshold and a generalized Pareto density in the tail for extreme value estimation. The proposed model is simple and flexible allowing us posterior density estimation and posterior inference for high quantiles. The model works well even for small sample sizes and in the absence of prior information. We evaluate the performance of the proposed model through a simulation study. Finally, the proposed model is applied to a real environmental data.