# Estimation and uncertainty quantification for extreme quantile regions

## TL;DR

This paper introduces Bayesian methods for estimating extreme quantile regions and quantifies the uncertainty of these estimates, outperforming existing approaches and demonstrated through simulations and pollution data analysis.

## Contribution

The paper develops novel Bayesian schemes for univariate and bivariate extreme quantile region estimation with uncertainty quantification, improving upon existing methods.

## Key findings

- Bayesian methods outperform existing approaches in simulations.
- Proposed methods effectively quantify uncertainty in extreme quantile estimates.
- Application to pollution data demonstrates practical utility.

## Abstract

Estimation of extreme quantile regions, spaces in which future extreme events can occur with a given low probability, even beyond the range of the observed data, is an important task in the analysis of extremes. Existing methods to estimate such regions are available, but do not provide any measures of estimation uncertainty. We develop univariate and bivariate schemes for estimating extreme quantile regions under the Bayesian paradigm that outperforms existing approaches and provides natural measures of quantile region estimate uncertainty. We examine the method's performance in controlled simulation studies. We illustrate the applicability of the proposed method by analysing high bivariate quantiles for pairs of pollutants, conditionally on different temperature gradations, recorded in Milan, Italy.