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Let us assume there are independently
measured values and
calibration constants
with their covariance matrix
. The latter
can also be theoretical parameters influencing the data, and
moreover they may be
correlated, as usually
happens if, for example, they are parameters of a calibration fit.
We can then include the in the vector that contains the
measurements and in the covariance matrix :

(6.44) 
The corrected quantities are obtained from the most general
function

(6.45) 
and the covariance matrix
from the covariance propagation
.
As a frequently encountered example, we can think of several
normalization constants, each affecting a subsample of the data 
as is
the case where each of several detectors
measures a set of physical quantities.
Let us consider just three quantities
() and three
uncorrelated
normalization standard uncertainties (
),
the first common to
and , the second to
and and the third to all three.
We get the following covariance matrix:

(6.46) 
Next: Use and misuse of
Up: Building the covariance matrix
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Giulio D'Agostini
20030515