Using Bayesian methods for extreme value analysis offers an alternative to frequentist ones, with several advantages such as easily dealing with parametric uncertainty or studying irregular models. However, computations can be challenging and the efficiency of algorithms can be altered by poor parametrization choices. The focus is on the Poisson process characterization of univariate extremes and outline two key benefits of an orthogonal parameterization. First, Markov chain Monte Carlo convergence is improved when applied on orthogonal parameters. This analysis relies on convergence diagnostics computed on several simulations. Second, orthogonalization also helps deriving Jeffreys and penalized complexity priors, and establishing posterior propriety thereof. The proposed framework is applied to return level estimation of Garonne flow data (France).

翻译：使用贝叶斯方法进行极值分析为频率学派方法提供了一种替代方案，具有易于处理参数不确定性或研究非正则模型等若干优势。然而，计算可能具有挑战性，且算法效率可能因参数化选择不当而受到影响。本文聚焦于单变量极值的泊松过程表征，并概述了正交参数化的两个关键优势。首先，当应用于正交参数时，马尔可夫链蒙特卡洛收敛性得到改善。该分析基于多个模拟计算的收敛诊断结果。其次，正交化还有助于推导杰弗里斯先验和惩罚复杂度先验，并建立其后验适定性。所提出的框架应用于加龙河流量数据（法国）的返回水平估计。