格点量子色动力学中高关联数据的协方差拟合
Covariance fitting of highly correlated data in lattice QCD
摘要：
我们解决了一个经常被问到的问题的协方差拟合的高度相关的数据，如我们的$B_K$数据的基础上SU（2）交错手征微扰理论。基本上，问题的本质是我们没有足够精确的拟合函数来拟合极其精确的数据。当协方差矩阵的特征值较小时，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。我们已经应用了一些处方，在市场上，如截断法，修改的协方差矩阵法，贝叶斯方法。我们还提出了一个全新的方法，本征模移位方法，它允许一个完整的协方差拟合，而无需修改协方差矩阵。在我们的例子中，本征模位移（ES）方法和贝叶斯方法是最好的处方的问题。我们还提供了一个数据分析的教学实例，其中对角近似和截断法明显拟合失败，但ES方法和贝叶斯方法工作得很好。
英文摘要：
We address a frequently asked question on the covariance fitting of the highly correlated data such as our $B_K$ data based on the SU(2) staggered chiral perturbation theory. Basically, the essence of the problem is that we do not have an accurate fitting function enough to fit extremely precise data. When eigenvalues of the covariance matrix are small, even a tiny error of fitting function yields large chi-square and spoils the fitting procedure. We have applied a number of prescriptions available in the market such as the cut-off method, modified covariance matrix method, and Bayesian method. We also propose a brand new method, the eigenmode shift method which allows a full covariance fitting without modifying the covariance matrix at all. In our case, the eigenmode shift (ES) method and Bayesian method turn out to be the best prescription to the problem. We also provide a pedagogical example of data analysis in which the diagonal approximation and the cut-off method fail in fitting manifestly, but the ES method and the Bayesian approach work well.
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