From: Don Groom (deg@lbl.gov)
Date: Thu Sep 30 2004 - 12:18:28 PDT
The following is a conjecture that I would like to look at further before
implementing in any analysis. The idea arises in connection with the pdf
note I recently distributed on the inappropriateness of fitting to
weighted-average points.
Suppose we have several images of an object obtained on the same night,
all of which have the same exposure time.
The usual deal is to take the variance as the number of electrons in
the object (SN aperture, or whatever). The intensity is the number of
electrons minus sky. [Never mind all the conversions and corrections for
now.]
However, this is not the true variance but our best estimator of the
variance based on a single image. Can we come up with a better estimator?
For convenience define the weight for the jth image on this night as
w_j = 1/\sigma_j^2. The the mean w for the night is \overbar w =
\sum w_j.
I suspect that \overline w is a better estimator of the weight than w_j.
If so, we are still making the approximation that the sky doesn't change
throughout the interval in which the images are obtained. But we can't
generalize to other nights, when the sky is likely to be different.
To be continued,
Don
|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|-+|
Don Groom (Particle Data Group, Supernova Cosmology Project)
DEGroom(at)lbl(dot)gov www-ccd.lbl.gov 510/486-6788 FAX: 510/486-4799
Analog: 50R6008//1 Cyclotron Road//Berkeley Lab//Berkeley, CA 94720-8166
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