AI 中文总结
该研究针对概率预测评估的多目标特性，提出IS-ROC曲线框架，结合几何方法实现预测校准与集成，为预测比较等提供了实用方案。
AI 中文摘要
概率预测评估本质上是多目标的，但现有的恰当评分规则将预测性能简化为单个标量值，可能掩盖预测集中度与预测精度之间的权衡。我们提出区间得分受试者工作特征（IS-ROC）曲线，这是一种图形框架，可表示通过调整预测紧密度生成的完整区间预测族。我们证明由数据生成过程诱导的IS-ROC曲线是帕累托最优且凸的，为最优预测前沿提供了几何表征。基于这些性质，我们提出一种基于切线优化和凸化的几何校准方法，以及一种通过凸包构造组合竞争预测器的集成策略。最后，我们提供实用工作流程和数值示例，说明在该框架内进行预测比较、校准和集成构造的过程。
英文摘要
Probabilistic forecast evaluation is inherently multi-objective, yet existing proper scoring rules reduce predictive performance to a single scalar value, potentially obscuring the trade-off between forecast concentration and predictive accuracy. We introduce the Interval-Score Receiver Operating Characteristic (IS-ROC) Curve, a graphical framework that represents the complete family of interval forecasts generated by varying prediction tightness. We show that the IS-ROC Curve induced by the data generating process is Pareto optimal and convex, providing a geometric characterization of the optimal forecasting frontier. Building on these properties, we propose a geometry-based calibration procedure based on tangent optimization and convexification, together with an ensemble strategy that combines competing forecasters through convex hull construction. Finally, we provide a practical workflow and numerical examples illustrating forecast comparison, calibration, and ensemble construction within the proposed framework.
Comments31 pages, 12 figures, 2 tables
