Combining extreme value theory with Bayesian methods offers several advantages, such as a quantification of uncertainty on parameter estimation or the ability to study irregular models that cannot be handled by frequentist statistics. However, it comes with many options that are left to the user concerning model building, computational algorithms, and even inference itself. Among them, the parameterization of the model induces a geometry that can alter the efficiency of computational algorithms, in addition to making calculations involved. We focus on the Poisson process characterization of extremes and outline two key benefits of an orthogonal parameterization addressing both issues. First, several diagnostics show that Markov chain Monte Carlo convergence is improved compared with the original parameterization. Second, orthogonalization also helps deriving Jeffreys and penalized complexity priors, and establishing posterior propriety. The analysis is supported by simulations, and our framework is then applied to extreme level estimation on river flow data.

翻译：将极值理论与贝叶斯方法相结合具有多项优势，例如量化参数估计的不确定性，或研究频率学派统计无法处理的非规则模型。然而，该方法在模型构建、计算算法乃至推断本身方面都留给用户众多选择。其中，模型的参数化方式会诱导出某种几何结构，在增加计算复杂度的同时可能降低计算算法的效率。我们聚焦于极值的泊松过程刻画，并概述正交参数化在解决上述两个问题中的两项关键优势。首先，多项诊断指标表明，与原始参数化相比，马尔可夫链蒙特卡洛收敛性得到改善。其次，正交化有助于推导杰弗里斯先验和惩罚复杂度先验，并建立后验合理性。通过仿真分析验证了该方法的有效性，随后我们将该框架应用于河流流量数据的极端水位估计。