From: Greg Aldering (aldering@panisse.lbl.gov)
Date: Mon Mar 24 2003 - 23:25:01 PST
On Sat, 22 Mar 2003, Robert A. Knop Jr. wrote:
> On Sat, Mar 22, 2003 at 05:12:02PM -0800, Greg Aldering wrote:
> > 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.
>
> Does this only happen once I'm fitting with a fixed zero, or does it
> happen even with the floating 0 but the new template?
>
> Fitting with a fixed zero could plausibly greatly reduce the uncertainty
> on the other parameters if there's a huge covariance between the zero
> level and the other parameters. If the zero level is fixed at zero,
> that may remove some of the freedom for the other parameters to vary.
>
> Note that the "primary fit" for this paper omits some of the worst
> offenders, and ends up with a rather better chisquare. The worst
> offenders that get thrown out are because their Ia status is in doubt:
> no real spectral confirmation.
Ok, in trying to ascertain to what extent changes in the quoted SN
uncertainties changed the chi-squared for each of Rob's fit procedures, I
did a full matrix comparing what the chi-squared would be for each fit if
the SN uncertainties of another fit were used instead.
P99 A-1 A-2 A-3 A-5
stroke stroke stroke stroke
errs errs errs errs errs
P99 fit 56.4 61.5 61.6 63.6 66.4
A-1 stroke fit 54.0 56.8 56.9 58.8 62.7
A-2 stroke fit 56.2 58.8 58.9 61.5 65.2
A-3 stroke fit 57.0 60.7 60.7 63.1 65.9
A-5 stroke fit 55.9 58.6 58.6 60.9 63.4
The diagonal terms are the chi-squareds of a given fit, using the
uncertainties of that lightcurve-fitting technique, and should equal the
values Rob quotes on his webpage. (In fact, they differ slightly.)
Interpreting the above under the assumption that only the errors changed
would say that the errors shrunk slightly for fit A-1 relative to P99, and
that there was also some shrinking of errors when going to A-3 and again
going to A-5. However, if you just look at the difference in the sum of
the squares of uncertainties between each fit relative to fit A-5 stroked,
you find that the uncertainties mostly shrunk in going to fit A-5 stroked.
This points out that some change in chi-squared in the above matrix must
come from changes in some SN which are accurately reflected by the quoted
uncertainties.
Although this makes it a little tough to use the chi-squared for each fit
as a hypothesis test, it doesn't really change the conclusion that it is
mainly the smaller quoted uncertainties for fit A-5 stroked which make its
chi-square worse than P99. (It is mildly interesting though that A-1
stroked has the best chi-square no matter which errors are used.)
- Greg
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