From: Greg Aldering (aldering@panisse.lbl.gov)
Date: Sun May 18 2003 - 10:20:47 PDT
>From robert.a.knop@vanderbilt.edu Sun May 18 06:49:53 2003
>To: Greg Aldering <aldering@panisse.lbl.gov>
>
>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)
Well, this should really be
max(|OM_lowext - OM_extcor| - sqrt(sigma_extcor^2 - sigma_lowext^2),0)
where sigma is the statistical error on the fitted value of OM.
>
>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....
Ok, take your example. If the true mean E(B-V) value happens to be
exactly 0, the errors in E(B-V) from N supernova can still displace the
measured mean value by sigma(R_B*E(B-V))/sqrt(N). Would you call that
offset a systematic? If E(B-V) uncertainties dominate the
extinction-corrected fit, than sigma_extcor comes almost directly
them, e.g., being of order R_B*E(B-V)/sqrt(N).
>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.
This is really the same thing. What you are saying is that due to a
lack of statistical accuracy in E(B-V), we can not eliminate the
possibility at better than 68% confidence that the high-redshift SNe
are not 0.06 mag brighter or 0.08 mag fainter than the low-redshift
SNe, due to dust. That is, since the R_B*E(B-V) offset is only 0.02
mag, you are basically using your statistical error on the colors and
calling it a systematic.
It seems to me that if we are converting our E(B-V) statistical errors
into systematic errors then we can't expect the statistical + dust
systematic errors of the low-extinction subset to be any better than
the statistical errors on the extinction-corrected fit. Am I missing
something here?
Given that, we have to reconsider what purpose the low-extinction subset
serves. We are using it because models tell us that there should be
a ridgeline of low-extinction. Therefore, we a supposing that as long
as we throw out extincted SNe, nature is guarenteeing similarity in
whatever small residual amount of extinction that remains. We have
tested whether this assumption holds for the low-extinction subset,
and we find that within our ability to measure, it does hold.
I would like to hear Saul's thoughts on this, as maybe I am not getting
what it is we want the extinction systematic to indicate.
- Greg
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