where we have marginalized the nuisance parameter α C . Here N S is the number of solar data points ( N S = 4 in the Rates Analysis and N S = 41 in the Global Analysis ) and N C = 14 is the number of CHOOZ data points . X 2 S is the solar least - squares function and V S is the corresponding covariance matrix , whose calculation in the Rates Analysis and in the Global Analysis is explained , respectively , in Sections 2.1 and 2.2 . X 2 C is the CHOOZ least - squares function and V C is the corresponding covariance matrix , whose calculation is explained in Section 2.1 .