数据分析中含关联系统误差的卡方函数的构造

CONSTRUCTION OF CHISQUARE FUNCTION INCLUDING CORRELATED SYSTEMATIC ERRORS IN DATA ANAYLSIS

含有多个误差项的卡方函数严格意义上应该表示成矩阵的形式,然而矩阵方法表示的卡方函数自由项较多,在使用计算机寻找卡方函数极值的过程变得相对困难。因此在实际构造的过程中,经常使用平方项的形式进行卡方函数的构造。基于原始的数据分析原理,可以证明这二者在数学上是等价的。

Data analysis based on chisquare function was a common statistical method in high energy physics experiments.The chisquare function including correlated systematic errors should be strictly expressed as a matrix.However the chisquare function would be much more complex to solve due to high degree of freedom.As a result,the chisquare function was constructed as squared term formulation in many actual experiments.Based on data analysis principle,these two methods are proved equivalent in mathematics.