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.

中文翻译：

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威尔克斯定理、全局拟合和中微子振荡

对中微子实验中出现的新物理模型的测试通常涉及对称为中微子振荡的量子力学效应的全局拟合。本文从了解使用对数似然和的更传统拟合方法开始，向学生介绍这些全局拟合中常用的方法。χ ²最小化。具体来说，我们讨论 Δχ ²，比较χ ²与新物理学的契合度χ ^{标准模型预测的2}部分，通常使用 Wilks 定理来解释。本文使用玩具模型来探索 Δ 的属性χ ²作为振荡函数的检验统计量。此类模型的统计数据显示偏离威尔克斯定理。新物理学的测试还经常检查数据子集的“张力”，称为“参数拟合优度”。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的概率的有效性。尽管我们选择了一个特定的场景——中微子振荡——来说明重要的观点，但学生应该记住，这些观点在将多个数据集拟合到复杂函数时广泛适用。