高度相关数据中协方差拟合的故障排除
Trouble shooting for covariance fitting in highly correlated data
摘要：
对于数据高度相关且协方差矩阵特征值较小时协方差拟合失败的问题，本文提出了一种可能的解决方案。作为一个例子，我们选择了高相关$B_K$数据的SU（2）交错手征微扰理论的基础上的数据分析。基本上，问题的本质是我们没有一个准确的拟合函数，因此我们无法拟合高度相关和精确的数据。当协方差矩阵的某些特征值较小时，即使拟合函数的微小误差也会产生较大的卡方，从而破坏拟合过程。我们应用了市场上的一些处方，如对角近似和截断法。此外，我们提出了一种新的方法，本征模移位方法微调的拟合函数，而保持不变的协方差矩阵。
英文摘要：
We report a possible solution to the trouble that the covariance fitting fails when the data is highly correlated and the covariance matrix has small eigenvalues. As an example, we choose the data analysis of highly correlated $B_K$ data on the basis of the SU(2) staggered chiral perturbation theory. Basically, the essence of the problem is that we do not have an accurate fitting function so that we cannot fit the highly correlated and precise data. When some eigenvalues of the covariance matrix are small, even a tiny error of fitting function can produce large chi-square and spoil the fitting procedure. We have applied a number of prescriptions available in the market such as diagonal approximation and cutoff method. In addition, we present a new method, the eigenmode shift method which fine-tunes the fitting function while keeping the covariance matrix untouched.
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