AI 中文总结
该研究通过耦合纤维丛的几何方法，阐明轮廓似然拟合中两种不确定性分解方法的区别，解释了高能物理中系统不确定性估计方法间的关系，明确了冗余参数影响与重复实验源方差不重合的原因。
AI 中文摘要
轮廓似然拟合中的不确定性分解通常通过冗余参数影响来报告，尽管拟合参数的偏移与约束该参数的观测波动所回答的是不同问题。最近，Pinto等人提出了一种基于观测波动的不确定性分解的明确构造，并认为该构造能更清晰地从物理源角度解释系统不确定性。我们通过使用一对耦合纤维丛，对两种方法的区别给出了几何描述。该几何方法阐明了高能物理中几种传统系统不确定性估计方法之间的关系，将轮廓化描述为信息正交水平提升，将舒尔补描述为感兴趣参数流形上的诱导度量；物理源不确定性通过将观测波动映射到得分余切向量、用逆总信息提升这些向量，并将所得估计量协方差向前推至感兴趣参数而产生。该构造解释了为何冗余参数影响通常与重复实验的源方差不重合。
英文摘要
Uncertainty decompositions in profile-likelihood fits are commonly reported through nuisance-parameter impacts, although shifting a fitted parameter and fluctuating the observation that constrains it answer different questions. Recently, Pinto et al. provided an explicit construction for uncertainty decomposition based on fluctuating the observations and argued that such a construction allows for a cleaner interpretation of systematic uncertainties in terms of physical sources. We provide a geometric description of the distinction between the two methods by using a coupled pair of fiber bundles. The geometrical approach clarifies the relationship between several methods traditionally used to estimate systematic uncertainties in high-energy physics. By describing the profiling as an information-orthogonal horizontal lift and the Schur complement as the induced metric on the parameter-of-interest manifold, physical-source uncertainties arise by mapping observation fluctuations to score covectors, raising them with the inverse total information, and pushing the resulting estimator covariance forward to the parameters of interest. This construction clarifies why nuisance-parameter impacts do not generally coincide with repeated-experiment source variances.
Comments15 pages, 5 figures
