Abstract A popular peaks-over-threshold (PoT) method of Extreme Value Theory to quantify the probabilities of rare events is examined here on data generated from a nonlinear random oscillator model, describing a qualitative behavior of rolling of a ship in irregular seas. The restoring force in the oscillator model has a softening shape associated with the ship rolling application, and the response is also made bounded, so as to eliminate the possibility of “capsizing.” As a result, the tail of the resulting probability density function of the response undergoes three regimes: the Gaussian core, the heavy tail and the short bounded tail. By considering several scenarios where data are available in one but not another regime, it is shown that the PoT method can produce unsatisfactory results. Some refined methods from Extreme Value Theory, for example, those based on mixture models, are also examined, but without much success. It is thus argued that a data-driven application of the PoT method may fail, if the physical aspects of the system under study are not taken into account.

中文翻译：

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数据驱动的峰值超过阈值分析的陷阱：来自极端船舶运动的观点

摘要 这里研究了一种流行的极值理论峰值阈值 (PoT) 方法来量化稀有事件的概率，该方法使用非线性随机振荡器模型生成的数据，描述了船舶在不规则海面中横摇的定性行为。振荡器模型中的恢复力具有与船舶横摇应用相关的软化形状，并且响应也有界，以消除“倾覆”的可能性。因此，所得到的响应概率密度函数的尾部经历了三种状态：高斯核心、重尾和短有界尾。通过考虑数据在一种而不是另一种情况下可用的几种情况，表明 PoT 方法可能会产生不令人满意的结果。极值理论中的一些精炼方法，例如，也对基于混合模型的那些模型进行了检查，但没有取得多大成功。因此，有人认为，如果不考虑所研究系统的物理方面，PoT 方法的数据驱动应用可能会失败。