From: Robert A. Knop Jr. (robert.a.knop@vanderbilt.edu)
Date: Sat Mar 08 2003 - 17:17:38 PST
I have great confidence in my fits which don't do E(B-V) corrections,
since I can reproduce the confidence intervals from P99.
However, in the last week I discovered a bug in my fits with E(B-V)
corrections that is turning out to make a pretty big difference.
(Basically, the bug made me ignore the E(B-V) correction and the
uncertainty on same for supernovae at z>0.7 which had a positive
E(B-V). This makes a pretty big difference in the uncertainties on the
cosmological parameters!)
Given this, I think it crucially important that somebody cross check my
cosmology fits. This is NOT an easy task; it took me a long time to get
to the point where I could reproduce the confidence intervals from P99,
because you have to be careful to include all of the "right" errors.
Hopefully, I can make this easier for you by enumerating exactly what
errors to include.
I *think* that what I'm doing is right now. I've been over this code
several times, and think that there aren't any more show-stopping bugs.
Still, it would be comforting if a completely different code confirmed
what I was doing.
I would ask that the person doing this first make sure he can reproduce
the P99 confidence intervals; I can send you a data file for that if you
need it. This is an important first step, because if you can't do this
than any discrepancies between your fits and mine won't be meaningful.
Next, make sure you can reproduce my non-E(B-V)-corrected confidence
intervals. Finally, try to confirm my E(B-V)-corrected confidence
intervals, using your own software and none of mine. Please don't come
to me with discrepancies until you're sure that you can reproduce the
P99 intervals, because again as I said that's a non-trivial task, and
should be the basic bar for any sort of cross-check.
Here's a list of the things which need to get included in the error
P99; add all these in quadrature. (Reference to variables can be
interpreted by looking at the header of the data summary table.)
* dmb
* an intrinsic 0.17 magnitudes of dispersion
* 5./log(10) * peculiarvel / (299792*z)
--> peculiarvel = 300 ... this is km/s
This format works for the no-H luminosity distance, with some
null assuption about OM and OL. It doesn't matter for higher z
supernovae, but can make a bit of a difference at low-z.
* 0.1*extinc (extinc being the MW extinction correction applied)
* alpha*dstret, where alpha is assumed to be 1.74 here
* sqrt(2.0*alpha*bcovars), where alpha is assumed to be 1.74 here
I believe that that's it. Note that in the tables you have. For fit
data, just fit z as x and mb+alpha*(stret-1) as y to the luminosity
distance equation. Marginalize over alpha, as that's a fit parameter
too. (So, really, mb is y, and the fit equation is the luminosity
distance minus alpha*(stret-1).) Also marginalize over script-M, as
described in our papers.
There was also a correlated zeropoint error, but this didn't make much
difference.
If you can get that to reproduce the P99 and my other contours, then add
in E(B-V). cc must be subtracted from mb. dcc must be added in
quadrature to the uncertainty on a given point. Additionally, if you're
good, you'll add Rb*bcovarcol*fac to the variance, where Rb is something
like 4.3, and fac is something close to 1. (Really, fac should be the
ratio between deb-v and dr-i.) Correlations between supernovae can make
a bigger difference when you E(B-V) correct, but let's not worry about
that for now. If we get the rest working, then we'll add that in.
-Rob
-- --Prof. Robert Knop Department of Physics & Astronomy, Vanderbilt University robert.a.knop@vanderbilt.edu
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