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.

极端分位数区域的估计是在极端情况分析中的一项重要任务，在这种空间中，未来极端事件可能以给定的低概率发生，甚至超出观测数据的范围。现有估计此类区域的方法，但没有提供任何估计不确定性的方法。我们开发了用于估计贝叶斯范式下的极端分位数区域的单变量和双变量方案，该方案优于现有方法并提供了分位数区域估计不确定性的自然度量。我们在受控仿真研究中检查了该方法的性能。我们通过分析在意大利米兰记录的有条件的不同温度等级条件下的成对污染物的高双变量分位数来说明该方法的适用性。