From: Robert A. Knop Jr. (robert.a.knop@vanderbilt.edu)
Date: Sun May 18 2003 - 06:49:52 PDT
On Sat, May 17, 2003 at 02:09:17PM -0700, Greg Aldering wrote:
> If you are correct that the spread in OM will be the quadrature difference
> between the low-extinction and the extinction-corrected fits, then you
> can simply take that quadrature difference as the statistical contribution
> to the difference in OM between the two fits. So then you systematic is
>
> |OM_lowext - OM_extcor| - sqrt(sigma_extcor^2 - sigma_lowext^2)
This doesn't make sense. What you're saying is that the E(B-V)
statistical errors in the extinction corrected fit contributes directly
to the offset between the non-extinction corrected and extinction
corrected fits. I don't see where that comes from.
The E(B-V) statistical errors contribute to why the extinction corrected
contours are *larger*, but not directly to any center offset. They will
probably contribute indirectly, because the asymmetric nature of the
OM_flat error means that puffy statistical errors tend to push
confidence regions away from the "no big bang" corner, but it's not
obvious how that would work, and I would expect it to be a lot smaller
than the simple quadrature difference you're talking about here.
Consider this toy case: pretend that the confidence regions are purely
symmetric (so there's no weird pushing away from the excluded region),
and that the mean E(B-V) value happens to be exactly 0. (It doesn't
need to be, given the uncertainties, but can be.) In that case, the two
confidence regions would fall almost exactly on top of each other; the
extinction corrected regions would just be larger. Clearly, though, the
extinction systematic isn't negative....
I think that the fairest simple thing to do is the 0.08-mag offset I was
talking about earlier. Our E(B-V) data indicates that that is the
1-sigma offset in the mean of the high redshift and low redshift sets
due to extinction.
I could probably do it better by Monte Carloing the offsets with a
1-sigma in the gaussian E(B-V) of 0.014 about 0.005 (or whatever it was)
for each high redshift supernova, and then doing 10 or 20 cases to find
the distributin of central OM values. The difference between mid+1sigma
of that distribution and the non-extinction-corrected OM would then be
the statistical error. I suspect that the mean result would be the same
as the simplistic offset I've done, but I could be wrong. (This would
also give us the asymmetric extinction systematic error bars.) I will
see if I can give this a try with a finite number of cases.
-Rob
-- --Prof. Robert Knop Department of Physics & Astronomy, Vanderbilt University robert.a.knop@vanderbilt.edu
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