A Semiparametric Bayesian Extreme Value Model Using a Dirichlet Process Mixture of Gamma Densities
This work addresses extreme value analysis for environmental and statistical applications, offering a flexible model that works with small samples and no prior information, though it appears incremental as it builds on existing Bayesian and extreme value methods.
The authors tackled extreme value estimation by proposing a semiparametric Bayesian model combining a Dirichlet process mixture of gamma densities for the bulk and a generalized Pareto density for the tail, enabling posterior density estimation and inference for high quantiles, with performance validated through simulation and application to environmental data.
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.