解释COMBO-17调查的距离相关性结果
Interpreting the Distance Correlation Results for the COMBO-17 Survey
摘要：
在大样本天体物理数据库的星系团中，星系的准确分类敏感地依赖于区分形态类型的能力，特别是在较高的红移。这种能力可以通过一种新的关联和相关性的统计测量来增强，称为{ \it距离相关系数}，它比两个变量之间线性关系的经典皮尔逊测量具有更大的统计能力来检测关联。距离相关测量提供了一个更精确的替代经典的措施，因为它是能够检测可能出现在天体物理应用的非线性关系。我们最近表明，距离和皮尔逊相关系数之间的比较可以有效地用于隔离各种星系数据集中的潜在离群值，并且这种比较能够确认与数据相关的准确性水平。在这项工作中，我们阐明了距离相关的优势时，适用于大型数据库。我们说明了如何可以有效地使用的距离相关措施作为一种工具，以确认在COMBO-17数据库中的各种变量之间的非线性关系，包括长轴和短轴的长度，以及替代红移分布。对于这些离群值对，距离相关系数通常高于皮尔逊系数，因为距离相关更容易检测到非线性关系。皮尔逊与距离相关系数的V形散点图也揭示了红移增加的模式以及每个红移范围内不同星系类型的贡献。
英文摘要：
The accurate classification of galaxies in large-sample astrophysical databases of galaxy clusters depends sensitively on the ability to distinguish between morphological types, especially at higher redshifts. This capability can be enhanced through a new statistical measure of association and correlation, called the {\it distance correlation coefficient}, which has more statistical power to detect associations than does the classical Pearson measure of linear relationships between two variables. The distance correlation measure offers a more precise alternative to the classical measure since it is capable of detecting nonlinear relationships that may appear in astrophysical applications. We showed recently that the comparison between the distance and Pearson correlation coefficients can be used effectively to isolate potential outliers in various galaxy datasets, and this comparison has the ability to confirm the level of accuracy associated with the data. In this work, we elucidate the advantages of distance correlation when applied to large databases. We illustrate how the distance correlation measure can be used effectively as a tool to confirm nonlinear relationships between various variables in the COMBO-17 database, including the lengths of the major and minor axes, and the alternative redshift distribution. For these outlier pairs, the distance correlation coefficient is routinely higher than the Pearson coefficient since it is easier to detect nonlinear relationships with distance correlation. The V-shaped scatterplots of Pearson versus distance correlation coefficients also reveal the patterns with increasing redshift and the contributions of different galaxy types within each redshift range.
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