证据、校准与稳定性：模型不确定性下假设检验的三元框架
Evidence, Calibration, and Stability: A Triadic Framework for Hypothesis Testing Under Model Uncertainty
浏览论文内容
中文总结 AI 辅助
本文提出ECS框架，将统计检验的证据、校准、稳定性三个角色分离并统一报告，推导相关稳定性半径与下界，经模拟验证其可带来不同解释，为模型不确定性下的假设检验提供形式综合方法。
中文摘要 AI 辅助
统计检验常被要求承担过多任务：单一报告结果需描述观测数据的含义、向读者保证重复抽样行为，且在工作模型受扰动时仍具说服力。这些任务相互关联但并不等价：费希尔归纳推理与奈曼-皮尔逊决策理论明确前两类任务，稳健检验、敏感性分析、脆弱性度量、多verse分析及分布稳定性方法则针对第三类任务。本文提出证据-校准-稳定性（Evidence-Calibration-Stability, ECS）框架，用于在报告各角色时保持其分离。其中，证据是后验数据，校准属于设计或程序范畴，稳定性是基准分析与声明模型邻域内可反转结论的扰动之间的后验数据距离。完整的ECS支持是合取的：任一坐标失效时，强坐标无法挽救。针对有限维仿射扰动，本文推导了精确椭球稳定性半径；针对光滑非线性边际，一致二次余项条件可在声明邻域内得到经认证的下界，以说明仿射公式何时仅为替代。本文还建立了坐标不变性与多声明的矩阵扩展，并区分确证性校准与描述性校准轮廓（当无法预先指定时）。对单样本t检验的模拟及Student的历史睡眠数据显示，三个坐标可导致不同解释。ECS是一种形式综合，并非声称证据、功效或稳健性本身为新内容。
英文摘要
Statistical tests are often asked to do too much. A single reported result is expected to describe what the observed data say, reassure readers about repeated-sampling behavior, and remain convincing when the working model is perturbed. Those tasks are connected, but they are not equivalent. Fisherian inductive inference and Neyman-Pearson decision theory clarify the first two; robust testing, sensitivity analysis, fragility measures, multiverse analysis, and distributional-stability methods speak to the third. I propose Evidence-Calibration-Stability (ECS) as a framework for keeping these roles separate while reporting them together. Evidence is post-data. Calibration belongs to the design or procedure. Stability is the post-data distance from the benchmark analysis to a conclusion-reversing perturbation within a declared model neighborhood. Full ECS support is conjunctive: a strong coordinate cannot rescue a failed one. For finite-dimensional affine perturbations, I derive an exact ellipsoidal stability radius. For smooth nonlinear margins, a uniform quadratic-remainder condition yields a certified lower bound over a declared neighborhood, showing when the affine formula is only a surrogate. I also establish coordinate invariance and a matrix extension for multiple claims, and distinguish confirmatory calibration from descriptive calibration profiles when prespecification is unavailable. Simulations for the one-sample t test and Student's historical sleep data show that the three coordinates can lead to different interpretations. ECS is a formal synthesis, not a claim that evidence, power, or robustness is itself new.
