Environmental extremes often show systematic variation with covariates. Three different nonparametric descriptions (penalized B-splines, Bayesian adaptive regression splines, and Voronoi partition) for the dependence of extreme value model parameters on covariates are considered. These descriptions take the generic form of a linear combination of basis functions on the covariate domain, but differ (i) in the way that basis functions are constructed and possibly modified, and potentially (ii) by additional penalization of the variability (e.g., variance or roughness) of basis coefficients, for a given sample, to improve inference. The three representations are used to characterize variation of parameters in a nonstationary generalized Pareto model for the magnitude of threshold exceedances with respect to covariates. Computationally efficient schemes for Bayesian inference are used, including Riemann manifold Metropolis-adjusted Langevin algorithm and reversible jump. A simulation study assesses relative performance of the three descriptions in estimating the distribution of the T-year maximum event (for arbitrary T greater than the period of the sample) from a peaks over threshold extreme value analysis with respect to a single periodic covariate. The three descriptions are also used to estimate a directional tail model for peaks over threshold of storm peak significant wave height at a location in the northern North Sea.

中文翻译：

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极端情况的灵活协变量表示

环境极端情况通常显示出具有协变量的系统变异。考虑了极值模型参数对协变量的依赖性的三种不同的非参数描述（惩罚 B 样条、贝叶斯自适应回归样条和 Voronoi 分区）。这些描述采用协变量域上基函数的线性组合的一般形式，但不同之处在于（i）构建和可能修改基函数的方式，并且可能（ii）通过额外的可变性惩罚（例如，方差或粗糙度）的基础系数，对于给定的样本，以改善推理。这三种表示用于表征非平稳广义帕累托模型中参数的变化，用于相对于协变量的阈值超出幅度。使用了贝叶斯推理的计算高效方案，包括黎曼流形 Metropolis-adjusted Langevin 算法和可逆跳跃。模拟研究评估了三种描述在估计 T 年最大事件分布（对于大于样本周期的任意 T）的相对性能，从峰值超过阈值极值分析相对于单个周期性协变量。这三种描述还用于估计北海北部某个位置超过风暴峰值有效波高阈值的峰值的定向尾部模型。模拟研究评估了三种描述在估计 T 年最大事件分布（对于大于样本周期的任意 T）的相对性能，从峰值超过阈值极值分析相对于单个周期性协变量。这三种描述还用于估计北海北部某个位置超过风暴峰值有效波高阈值的峰值的定向尾部模型。模拟研究评估了三种描述在估计 T 年最大事件分布（对于大于样本周期的任意 T）的相对性能，从峰值超过阈值极值分析相对于单个周期性协变量。这三种描述还用于估计北海北部某个位置超过风暴峰值有效波高阈值的峰值的定向尾部模型。