物理测量的信息损失位置估计与曲率尺度分析：高斯、柯西和逻辑斯蒂中子寿命基准
Information-Loss Location Estimation and Curvature-Scale Analysis of Physical Measurements: A Gaussian, Cauchy, and Logistic Neutron-Lifetime Benchmark
- Canadian Nuclear Laboratories（加拿大核实验室）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对分布未知的重复物理测量，提出基于信息损失和曲率规则的两步位置-尺度估计法，统一高斯、柯西、逻辑斯蒂分布，并在中子寿命基准上给出三个位置估计值。
AI中文摘要：
我们开发并实现了一种针对重复物理测量的两步位置-尺度分析方法，适用于底层分布未知的情形。对于选定的替代分布，在固定尺度下总体Kullback-Leibler信息损失的平稳性激发了位置评分，我们通过经验交叉熵将其应用于观测测量值。随后，Steiner曲率规则单独定义了伴随的尺度。我们将高斯、柯西和逻辑斯蒂替代分布置于一个统一的框架中，并在一个物理基准上可重复地实现它们。对于逻辑斯蒂替代分布，我们将已建立的有界位置评分与由曲率规则定义的尺度配对，而非使用拟合的调优常数或尺度似然方程。对于具有不同引用不确定度的高斯测量，实验级别的曲率约定和明确的方差映射给出了与加权拟合的标准残差方差估计的精确代数联系。应用于已发表的包含21个测量值的中子寿命汇编，逆方差加权、最频值和逻辑斯蒂位置分别为878.689秒、881.164秒和882.835秒。这些数值是所比较构造的基准结果，并非作为新的推荐中子寿命提出。
英文摘要：
We develop and implement a two-step location-scale analysis for repeated physical measurements when the underlying distribution is not known. For a chosen substitute distribution, stationarity of population Kullback-Leibler information loss at fixed scale motivates the location score, which we apply to the observed measurements through empirical cross-entropy. Steiner's curvature rule then defines a companion scale separately. We place Gaussian, Cauchy, and logistic substitutes in one common construction and implement them reproducibly on a physics benchmark. For the logistic substitute, we pair the established bounded location score with a scale defined by the curvature rule rather than by a fitted tuning constant or a scale-likelihood equation. For Gaussian measurements with different quoted uncertainties, an experiment-level curvature convention and a stated variance mapping give an exact algebraic connection to a standard residual-based variance estimate for a weighted fit. Applied to a published 21-measurement neutron-lifetime compilation, the inverse-variance weighted, most frequent value, and logistic locations are 878.689, 881.164, and 882.835 s, respectively. These values are benchmark results of the compared constructions and are not proposed as a new recommended neutron lifetime.
