分离比模型拟合中的过拟合和相关性
Overfitting and correlations in model fitting with separation ratios
摘要：
$r_{01}$和$r_{10}$分离比不是独立的，因此将它们组合到单个序列$r_{010}$中会过拟合数据，这可能导致具有非常大的条件数的几乎奇异的协方差矩阵，从而在比较模型和观测值时产生虚假结果。由于$r_{02}$比值与$r_{10}$和$r_{01}$比值密切相关，因此应将其合并为单个系列$r_{102}$（或$r_{012}$），该系列未过度拟合，并使用合并集的协方差矩阵$cov_{102}$（或$cov_{012}$）比较模型和观察值。我通过将修正后的遗产项目数据与我在10颗开普勒恒星上的结果进行比较来说明这些观点。
英文摘要：
The $r_{01}$ and $r_{10}$ separation ratios are not independent so combing them into a single series $r_{010}$ is overfitting the data, this can lead to almost singular covariance matrices with very large condition numbers, and hence to spurious results when comparing models and observations. Since the $r_{02}$ ratios are strongly correlated with $r_{10}$ and $r_{01}$ ratios, they should be combined into a single series $r_{102}$ (or $r_{012}$), which are not overfitted, and models and observation compared using the covariance matrix $cov_{102}$ (or $cov_{012}$) of the combined set. I illustrate these points by comparing the revised Legacy Project data with my results on the 10 Kepler stars in common.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
