Dissimilarity measures in detrital geochronology
Dissimilarity measures in detrital geochronology
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DOI：
10.1016/j.earscirev.2017.11.027
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发表时间：
2017-12
影响因子：
12.1
通讯作者：
P. Vermeesch
中科院分区：
文献类型：
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作者：
P. Vermeesch
对碎屑年龄分布之间的（不）相似性进行量化的能力是沉积物源研究的一个重要方面。本文回顾了三种不同的方法来做到这一点。第一类相异性度量基于参数假设检验，例如t或卡方检验。这是为了客观地决定两个样本是否来自同一个群体。尽管此类测试在理论上可能很有吸引力，但在实践中，它们对沉积地质学家的价值有限，因为它们的结果取决于样本量。与此相反，上述测试的效果大小是独立的样本量，可以作为一个客观点之间的比较碎屑年龄分布。这种方法的主要局限性是它需要合并或平均，这会丢弃有价值的信息。第二类相异性度量是基于非参数假设检验，例如Kolmogorov-Smirnov检验。这些方法不需要对数据进行预处理，并且能够捕捉年龄分布之间更细微的差异。不幸的是，非参数检验没有明确定义的样本效应量，因此不可能将其用作独立于样本量的绝对比较点。然而，非参数相异度测量可用于量化样品之间的相对差异。第三类相异性措施的目的是考虑到年龄测定的分析不确定性。相似性和互相关系数是基于概率密度图（PDP）的自组织相异性度量。这些应用窄平滑内核精确的数据，和广泛的平滑内核不精确的数据。相比之下，Sircombe-Hazelton L2范数使用核函数估计（KFE），其使用与PDP完全相反的策略。它们将宽平滑核应用于精确数据，将窄平滑核应用于不精确数据。本文表明，基于KFE的方法产生合理的结果，而相似性和互相关的方法没有。KFE方法增加的复杂性只值得在联合收割机上获得的数据与巨大变化的分析精度相结合的研究中付出努力。在大多数情况下，没有必要考虑到碎屑年龄分布的分析不确定性。样本效应量、非参数统计量或L2范数可用于通过多维标度（MDS）以图形方式比较样本。与以前的主张不同，这些措施不需要为此目的独立于样本量。
The ability to quantify the (dis)similarity between detrital age distributions is an essential aspect of sedimentary provenance studies. This paper reviews three different ways to do this. A first class of dissimilarity measures is based on parametric hypothesis tests such as the t- or chi-square test. These are designed to objectively decide whether two samples were derived from a common population. Appealing though such tests may appear in theory, in practice they offer limited value to sedimentary geologists because their outcome depends on sample size. In contrast, the effect size of said tests is independent of sample size and can be used as an objective point of comparison between detrital age distributions. The main limitation of this approach is that it requires binning or averaging, which discards valuable information. A second class of dissimilarity measures is based on non-parametric hypothesis tests such as the Kolmogorov-Smirnov test. These do not require pre-treatment of the data and are able to capture more subtle differences between age distributions. Unfortunately, non-parametric tests do not have well defined sample effect sizes and so it is not possible to use them as an absolute point of comparison that is independent of sample size. Nevertheless, non-parametric dissimilarity measures can be used to quantify the relative differences between samples. A third class of dissimilarity measures aims to account for the analytical uncertainties of the age determinations. The likeness and cross-correlation coefficients are ad-hoc dissimilarity measures that are based on Probability Density Plots (PDPs). These apply a narrow smoothing kernel to precise data, and a wide smoothing kernel to imprecise data. In contrast, the Sircombe-Hazelton L2-norm uses Kernel Functional Estimates (KFEs), which use exactly the opposite strategy as PDPs. They apply a wide smoothing kernel to precise data, and a narrow smoothing kernel to imprecise data. This paper shows that the KFE-based approach produces sensible results, whereas the likeness and cross-correlation methods do not. The added complexity of the KFE approach is only worth the effort in studies that combine data acquired on equipment with hugely variable analytical precision. In most cases, there is no need to account for the analytical uncertainty of detrital age distributions. The sample effect size, non-parametric statistics, or L2-norm can be used to graphically compare samples by Multidimensional Scaling (MDS). In contrast with previous claims, there is no need for these measures to be independent of sample size for this purpose.