From: Robert A. Knop Jr. (robert.a.knop@vanderbilt.edu)
Date: Wed Feb 19 2003 - 15:11:48 PST
On Wed, Feb 19, 2003 at 03:03:28PM -0800, Lifan Wang wrote:
> One thing I am not clear is the problem with having all the SNe with
> floating base line. I expect having an extra parameter only to reduce
> the fitting errors, although the best fit may prove to be quite
> irrelavent, the fit itself should always be an improvement. So can
> you please explain what is exactly bothering you here.
Too much freedom sometimes gives it really screwy fits. I can look for
an example, but some of the low-redshift supernove came up with fits
that didn't make much sense. This is generally true when fitting
things; if you give it *too many* parameters, it can find a fit which is
too good. (Consider fitting a line to three data points. If you
instead fit a parabola, you'll get an "improved" fit with much smaller
errors and residuals, but if there is any scatter in the points, you
will have a much *worse* (i.e. overdetermined) estimate of the slope
trend of the data. This is an extreme example, but it does point out
the fallacy of the idea that "more parameters means better fit".)
Additionally, as I've been trying to say, it doesn't make sense to treat
the HST supernovae that way. By allowing the baseline to float, you're
saying that you've slightly missubtracted the host galaxy. Well, if
you've missubtracted the host galaxy, then you've also incorrectly mixed
the HST and ground based data together-- the mixing used the mutual
zeropoints to get a ratio between HST and ground based lightcurves so as
to produce one lightcurve of a given color (R or I). As such, you must
believe that what you're multiplying is a flux of just the supernova,
not the supernova plus some host. The amount of host included in an HST
aperture is *far* less than the amount of host included in a ground
aperture. (And, indeed, given variable seeing, the amount of host
included in a ground aperture isn't internally consistent.) To be
consistent with these assumptions, you should then fit with a fixed
zero, unless you have no choice (which is the case for a handful of P99
supernovae with no I-band final reference).
There is no best way to do this; I've done the best we can.
> For 92ag, I am surprised and bothered by the fact that your best fit
> needs a baseline offset of only 0.03. It seems to me that your other
> fit (with fixed baseline) actully did not converge to the real minimum
> chi^2. One way to see this is to add 0.03 to your best fit (with floating
> zero baseline) which then gives a fit with the baseline fixed to zero.
> Visually, I would expect this to be a much better fit than the fit given
> in the figure with fixed zero.
I really think what's going on is that those low points are driving the
curve far more than they ought to. There's a whole bunch of them, with
really tiny error bars, down there.
In the end, I don't think that any of this haggling is going to affect
the results much. Look at the figure that compares the P99 confidence
intervals to my refits of the same data. My refits include the new
lightcurve fits as well as new K-corrections. Any sort of tuneups we do
on this sort of thing is going to make *less* difference than that, but
will take a lot of time.
We have to choose: do we want to try to converge toward perfection, or
do we want to publish the paper? Because those are two inconsistent
goals.
-Rob
-- --Prof. Robert Knop Department of Physics & Astronomy, Vanderbilt University robert.a.knop@vanderbilt.edu
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