论文标题
威尔克斯定理，全球拟合和中微子振荡
Wilks's Theorem, Global Fits, and Neutrino Oscillations
论文作者
论文摘要
中微子实验中出现的新物理学模型的测试通常涉及全局拟合，适合称为中微子振荡的量子机械效应。本文向学生介绍了这些全局拟合中常用的方法，从使用日志样式的了解更常规的拟合方法和$χ^2 $最小化开始。具体来说，我们讨论了如何使用Wilks的定理来解释$Δχ^2 $与新物理学的$χ^2 $与标准模型预测的$χ^2 $进行比较。本文使用玩具模型来探索$Δχ^2 $的属性，作为振荡功能的测试统计量。此类模型的统计数据显示出偏离威尔克斯定理。新物理学的测试还经常检查数据子集的“张力”，称为“拟合的参数优点”。在本文中，我们解释了这种方法，并使用玩具模型来检查该测试概率的有效性。尽管我们选择了一种特定的方案 - 中微子振荡 - 以说明要点，但学生应该记住，在将多个数据集拟合到复杂功能时，这些点广泛适用。
Tests of models for new physics appearing in neutrino experiments often involve global fits to a quantum mechanical effect called neutrino oscillations. This paper introduces students to methods commonly used in these global fits starting from an understanding of more conventional fitting methods using log-likelihood and $χ^2$ minimization. Specifically, we discuss how the $Δχ^2$, which compares the $χ^2$ of the fit with the new physics to the $χ^2$ of the Standard Model prediction, is often interpreted using Wilks's theorem. This paper uses toy models to explore the properties of $Δχ^2$ as a test statistic for oscillating functions. The statistics of such models are shown to deviate from Wilks's theorem. Tests for new physics also often examine data subsets for "tension" called the "parameter goodness of fit". In this paper, we explain this approach and use toy models to examine the validity of the probabilities from this test also. Although we have chosen a specific scenario -- neutrino oscillations -- to illustrate important points, students should keep in mind that these points are widely applicable when fitting multiple data sets to complex functions.
