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, computation can be challenging and the efficiency of algorithms can be altered by poor modelling choices, and among them the parameterization is crucial. We focus 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. Our framework is applied to return level estimation of Garonne flow data (France).

翻译：采用贝叶斯方法进行极端值分析为频率学派方法提供了替代方案，具有易处理参数不确定性及研究非正则模型等多项优势。然而，计算过程可能具有挑战性，不当的建模选择会降低算法效率，其中参数化选择尤为关键。本研究聚焦于单变量极值的泊松过程刻画，提出正交参数化的两个核心优势：首先，应用于正交参数时马尔可夫链蒙特卡洛收敛性得到改善，该结论基于多个模拟计算的收敛诊断分析；其次，正交化有助于推导杰弗里斯先验与惩罚复杂度先验，并确立其后验适定性。本框架已应用于法国加龙河流量数据的重现水平估算。