Omnivariant Generalized Least Squares regression: Theory, geochronological applications, and making the case for reconciled ?47 calibrations
Omnivariant Generalized Least Squares regression: Theory, geochronological applications, and making the case for reconciled ?47 calibrations
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全变量广义最小二乘回归：理论、地质年代学应用以及协调 47 校准的案例
DOI：
10.1016/j.chemgeo.2023.121881
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发表时间：
2024
期刊：
影响因子：
3.9
通讯作者：
Daëron M
中科院分区：
文献类型：
--
作者：
Daëron M
最小二乘回归方法在数学上是强大的，概念和计算简单，并广泛应用于许多领域。然而，常用的最小二乘回归方法（如约克回归或广义最小二乘（GLS））都没有考虑所有观测（x，y）值之间的完整协方差集。在这里，我们描述了全变广义最小二乘（OGLS）方法来拟合模型的formy=f（x），占（x，y）数据的完整的误差相关结构，基于一阶线性传播的不确定性在所有变量的误差inyrasidas，其次是最小化的向量ofyrasidas相对于马氏范数定义的协方差矩阵。这种方法可以被描述为约克回归和GLS的推广。它在数学上对直线拟合是精确的，也适用于许多非线性模型。在这里，我们描述了OGLS回归的原理，讨论了它的属性、注意事项和实际使用，并提供了两个一致的Python和R开源实现。为了说明地质年代学和稳定同位素地球化学的各个领域如何从这种新方法中受益，我们讨论了OGLS如何具体应用于40 Ar/39 Ar定年，以及它如何提供强大的数学证据，证明最近定义的I-CDES刻度中的Δ 47碳酸盐校准在统计上是不可区分的，有效地解决了长期存在的方法差异。
Least-squares regression methods are mathematically powerful, conceptually and computationally simple, and widely used in many fields. However, none of the commonly-used flavors of least-squares regression, such as York regression or Generalized Least Squares (GLS), take into account the full set of covariances between all observed (x,y) values. Here we describe the Omnivariant Generalized Least Squares (OGLS) method to fit a model of the formy=f(x), accounting for the full error correlation structure of the (x,y) data, based on a first-order linear propagation of the uncertainties in all variables into errors inyresiduals, followed by minimizing the vector ofyresiduals with respect to the Mahalanobis norm defined by its covariance matrix. This approach may be described as a generalization of both York regression and GLS. It is mathematically exact for straight-line fits, and is also suitable for many non-linear models. Here we describe the principles of OGLS regression and discuss its properties, caveats, and practical use, and provide two consistent open-source implementations in Python and R. To illustrate how various fields of geochronology and stable-isotope geochemistry may benefit from this new method, we discuss how OGLS may specifically apply to40Ar/39Ar dating and how it provides robust mathematical evidence that Δ47carbonate calibrations in the recently defined I-CDES metrological scale are statistically indistinguishable, effectively solving long-standing methodological discrepancies.