For each **data** set i and energy group m a systematic errorη i,m is estimated by:
η i,m = 1 n i ni j=1 (y ij,m − f (E j,m , θ)),(22)
where y ij,m are the **data** belonging to the **data** set i with energies E j belonging to the energy group m. These values are used to provide estimates of the systematic error η m for each energy group m:
η m = 1 K K i=1η i,m ,(23)
together with its covariance matrix C η . The diagonal and off-diagonal terms of this matrix, which are denoted by C η,mm and C η,m1m2 , respectively, are given by:
C η,mm = 1 K − 1 K i=1 (η i,m −η m ) 2(24)
and
C η,m1m2 = 1 K K i=1η i,m1ηi,m2 −η m1ηm2 ,(25)
with a constraint that:
C η,m1m2 ≤ min [C η,m1m1 , C η,m2m2 ].(26)
The variance of the distribution of the random error for a given **data** set i and energy group m is estimated from the formulâ
σ 2 i,m = 1 n i − 1 ni j=1 (y ij,m −f (E j,m , θ)−η i,m ) 2 . (27)
These values form a covariance matrix D with only diagonal terms reflecting the contribution of random effects due to, e.g., counting statistics.