From: Robert A. Knop Jr. (robert.a.knop@vanderbilt.edu)
Date: Sun May 18 2003 - 10:47:16 PDT
On Sun, May 18, 2003 at 10:20:47AM -0700, Greg Aldering wrote:
> 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).
Yes, I would call that offset a systematic -- in that it represents the
limit of our knowledge on the true E(B-V) distribution.
> 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?
No, I think you're right-- if we do it right (given my current
understanding of "right"), the extinction systematic should be
comparable in size to the statical error bar on the extinction-corrected
fit.
> 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.
The systematic then comes from the leftover slop in that "ability to
measure"-- i.e. to our ability to measure, the HST supernovae have the
same extinction as the low-z SNe (in the low-extinction subset) to
within 0.015 magnitudes. Same for the P99 SNe and 0.025 magnitudes.
Unless we want to put in some sort of prior assumption on the intrinsic
extinction distribution for purposes of evaluating the systematic, then
we can't do any better than that uncertainty of 0.015 or 0.025
magnitudes-- which is going to give us something like an 0.1 systematic
uncertainty in the flat-universe value of Omega_M on the low-extinction
subset. I'd like to avoid putting in a prior assumption, after we spend
all that time in the paper trying to discourage that sort of thing when
doing statistical E(B-V) corrections.
Note that, of course, the size of both the statistical and systematic
error bars goes down if you use a lower R_B.
-Rob
-- --Prof. Robert Knop Department of Physics & Astronomy, Vanderbilt University robert.a.knop@vanderbilt.edu
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