From: Greg Aldering (aldering@panisse.lbl.gov)
Date: Sat Mar 22 2003 - 17:12:02 PST
Analysis of the residuals that Rob provided for his fits A-1 through A-5
show that the full increase in chi-squared can be ascribed to the change
in the *uncertainties* quoted for each SN. Here is what I find:
Original P99 fit has Chi-squared = 56.4
A-5 fit, with all of Rob's changes has Chi-squared = 63.4
A-5 fit, but using the uncertainties from P99 has Chi-squared = 55.9
(The number of SN was the same, 53, in all cases.)
So, it is not the technique that is making Chi-squared worse in going from
fit A-1 to A-5, but rather, the fact that Rob quotes smaller
uncertainties. (Granted, the smaller uncertainties might be related to the
technique, but there are many components to the overall statistical error
budget.)
There are a few SNe which account for a good fraction of this difference,
94361, 9579, 9624, and 9794. But, an equal contribution comes from all the
very small changes in quoted uncertainty for lots of SNe at all redshifts.
Note that there is no obvious redshift-dependent pattern in the changes in
chi-square for each SN, suggesting that the changes have more to do with
the specifics of the data for each SN than with how low vs high, or R-->B
vs R-->U corrections or fitting styles are performed.
For 94361, 9579, 9624, and 9794, there is no obvious clue from the
SNminuit fit chi-square ratios Rob lists as to why the uncertainties
would change by much.
Anyway, if we can understand the changes in the quoted uncertainties and
they make sense, then one could argue that on the basis of chi-squared
the A-5 fits perform as well as the P99 fits. (The poor chi-squared/DOF is
a different story, assuming Rob's uncertainties hold up.)
- Greg
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