Sensitivity measures based on scoring functions
提出一个通用框架，利用评分函数构造任何可提取函数T的敏感性度量，量化预测精度的相对提升，并通过Murphy图展示所有度量，适用于均值、风险值等函数。
We propose a holistic framework for constructing sensitivity measures for any elicitable functional T of a response variable. The sensitivity measures, termed score-based sensitivities, are constructed via scoring functions that are (strictly) consistent for T. These score-based sensitivities quantify the relative improvement in predictive accuracy when available information, e.g., from explanatory variables, is used ideally. We establish intuitive and desirable properties of these sensitivities and discuss advantageous choices of scoring functions leading to scale-invariant sensitivities. Since elicitable functionals typically possess rich classes of (strictly) consistent scoring functions, we demonstrate how Murphy diagrams can provide a picture of all score-based sensitivity measures. We discuss the family of score-based sensitivities for the mean functional (of which the Sobol indices are a special case) and risk functionals such as Value-at-Risk, and the pair Value-at-Risk and Expected Shortfall. The sensitivity measures are illustrated using numerous examples, including the Ishigami–Homma test function. In a simulation study, estimation of score-based sensitivities for a non-linear insurance portfolio is performed using neural nets.