From: Lifan Wang (lifan@panisse.lbl.gov)
Date: Wed Feb 19 2003 - 15:43:12 PST
Rob,
I totally agree that it is impossible to make this perfect. But
you did not answer my question of if the fixed slope fit of the 92ag has
converged. So I am attaching my arguement below that it did not converge.
> > 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.
>
From your figure the chi2 for 92ag are
| fixed base | floating base
chi2 | 1.35e+03 | 101.
dof | 29. | 31.
Now, shift the best fit of the floating case by 0.034 to restore the
case with the base fixed to zero. What is the chi2 of such a fit ?
Let Xi be the ith model data points, Mi the ith model points of
the one with floating base
chi2 = sum((Xi-Mi)^2/error_i^2)
Now remove the 0.03 offset, the chi^2 is
chi^2 = sum((Xi-Mi-0.03)^2/error_i^2)
= sum((Xi-Mi)^2/error_i^2) + sum(0.03^2/error_i^2) +
2.*sum((Xi-Mi)*0.03/error_i^2)
The last term should be zero for a correct fit ==>
chi^2 = sum((Xi-Mi)^2/error_i^2) + sum(0.03^2/error_i^2)
~ 101. + sum(0.03^2/error_i^2)
This chi^2 is apparently much less than 1.35e+03. So I do not think
the fit with fixed baseline has converged.
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