发表机构
INFN, Sezione di Padova; Luleå University of Technology（意大利国家核物理研究所帕多瓦分部; 吕勒奥理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究揭示协方差矩阵替代统计模型会改变似然比排序，导致置信决策变化，并量化了覆盖盲点处的显著差异。
AI 中文摘要
协方差矩阵常被用作测量统计模型的紧凑替代。我们表明，这种替代不仅会改变拟合值或其不确定性，还会改变实验本身的似然比排序。在一个可处理的关联测量模型中，数据分为信息性分量和辅助残差异议。因此，精确似然推断不使用该差异，而数据依赖的协方差矩阵和非线性变换后的高斯重构可将其重新引入参数推断。我们通过等校准接受区域的对称差的概率质量来量化由此产生的变化——即重复实验中关于测试参数值的置信决策发生改变的比例。在小不确定性区域，排序差异通常与总相对不确定性呈一阶关系，而常规和辅助条件覆盖缺陷则始于二阶。在“覆盖盲”点，领先覆盖差异消失，而排序差异保持非零。在一个具有10%总相对不确定性的代表性盲例中，约7.6%的实验改变其置信决策，尽管两种程序均精确校准。同一机制将Peelle的相关难题与关于辅助性和相关子集的经典文献联系起来：协方差近似可为真实模型中辅助的拟合优度统计量制造推断相关性。我们直接展示了这如何改变针对相同信息内容报告的置信区间，并将分析扩展到不等统计不确定性和双测量情形之外。
英文摘要
A covariance matrix is often used as a compact surrogate for the statistical model of a measurement. We show that this replacement can change not only a fitted value or its uncertainty, but also the likelihood-ratio ordering of the experiment itself. In a tractable correlated-measurement model, the data separate into an informative component and an ancillary residual disagreement. Exact likelihood inference therefore does not use that disagreement, whereas data-dependent covariance matrices and Gaussian reconstructions after nonlinear transformations can reintroduce it into parameter inference. We quantify the resulting change by the probability mass of the symmetric difference of equally calibrated acceptance regions - the fraction of repeated experiments for which the confidence decision about a tested parameter value changes. In the small-uncertainty regime the ordering discrepancy is generically first order in the total relative uncertainty, whereas conventional and ancillary-conditioned coverage defects begin at second order. At 'coverage-blind' points the leading coverage difference vanishes while the ordering discrepancy remains nonzero. In a representative blind case with 10% total relative uncertainty, about 7.6% of experiments change their confidence decision despite exact calibration of both procedures. The same mechanism connects Peelle's Pertinent Puzzle to the classical literature on ancillarity and relevant subsets: a covariance approximation can manufacture inferential relevance for a goodness-of-fit statistic that is ancillary in the true model. We show directly how this changes the confidence interval reported for the same informative content, and extend the analysis beyond equal statistical uncertainties and beyond the two-measurement case.
Comments34 pages, 8 figures
