From: Greg Aldering (aldering@panisse.lbl.gov)
Date: Sat May 17 2003 - 14:09:17 PDT
>On Sat, May 17, 2003 at 01:35:40PM -0700, Greg Aldering wrote:
>> I believe that correct way to isolate the E(B-V) uncertainties is to
>> Monte Carlo only the E(B-V) errors and then look at the distribution of
>> best-fit values of Om in a flat universe. This would be very time
>> consuming if you let script M and alpha vary, since you have to
>> marginalize over their probabilities. A fast, but less accuract way
>> would be to let MINUIT or some other solver crank out the best-fit
>> values based on the equations for Om, script M, and alpha (with Ol =
>> 1-Om).
>
>Are you talking about in the extinction-corrected fit? If so, that
>ought to just give approximately a spread of OM which is the same as the
>spread we get by using the current error bars in the chisquare fit.
>(That is, if we treat the errors as Gaussian.) This is assuming you're
>talkinging about Monte Carloing each SN's EBV based on its dEBV. Or,
>probably more accuratley, it will give you a spread which is the
>quadrature difference between the dOM size from the extinction-corrected
>and not-extinction-corrected fits; very close, anyway. It's not clear
>to me, though, how measuring the size of that spread tells us what the
>extinction systematic ought to be for a non-extinction-corrected fit; it
>only tells us how much of the statistical uncertainty in the extinction
>corrected fit comes from color errors.
Yes, I am talking about Monte Carloing each SN's EBV based on its dEBV.
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)
Of course this is an approximation because sigma_lowext is higher than it
would be if the low-extinction fit had as many SNe as the extinction-corrected
fit. You could simply account for that by assuming that
sigma_lowext' = sigma_lowext * sqrt(N_lowest/N_extcor)
and using sigma_lowext' in place of sigma_lowext in the previous equation.
The sqrt(N_lowest/N_extcor) factor must be quite close to 1.
- Greg
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