From: Robert A. Knop Jr. (robert.a.knop@vanderbilt.edu)
Date: Mon May 19 2003 - 05:28:42 PDT
Some thoughts --
P. 3, second comment. I don't think we *need* to distinguish from the
priored extinction correction here. We have "unbiased" in there, which
is all that's necessary. We beat that to death later. I wouldn't
change anything in that sentence.
P. 13: I put that in because Greg was confused about the blue side. IT
looks like it didn't work, because you are also confused. Here's the
deal: error bars are on points. Reddening means that points can be
redder than the fit, or (equivalently) that the fit can be bluer than
the points. Thus, you want more freedom on the error bar that's on the
*blue* side of the point, *not* on the red side of the point. The
latest iteration didn't use an error bar of a different size on each
side, but did use the "stretchy" error bar. I can just describe that
and not use the word extendable if you don't like it.
P. 18, right column. I agree with Greg. We don't need to take credit
for the Bayesian prior; not only don't we want to, but that's a bit
disingenuous because the *only* reason it was in that paper was in
reaction to Riess. Let's leave this the way it is, where we say Riess
did it, and mention Fit E in P99 later. Re: a paragraph describing why
the Hatano prior isn't crazy, I can't write that, because I have a
gut-feeling belef it *is* crazy. I haven't read Hatano, but just
looking at my E(B-V) vs. s distribution for the low-redshift supernovae
shows me that there are lots of supernovae at relatively high
extinction, more so than I would intuitively expect from looking at the
Hatano prior. (I would have to look more carefully; probably something
with a huge peak at 0 and a long tail does make sense, but I haven't
thought enough to know if I believe that that tail is high enough.)
Moreover, as Don is always reminding us, using a prior like that is
*always* crazy because you're losing track of the difference between
measurement uncertainties and the intrinsic distribution.
In any event, even if the prior itself may be likely to describe a true
E(B-V) distribution, I would really rather not spend any doing anything
that sounds like defending use of this prior in E(B-V) corrections. If
we are going to put something in defending the use of a low-extinction
set as likely to be unreddened due to the Hatano information, let's put
that in a different place to clearly distinguish that approach from
something that might look like it's defending the Riess 1998 approach.
Page 21: I'd sort of like to leave a reference to the Phillips RB in
there, because I believe that a lower RB is almost certainly going to
figure into the future of extinction corrected supernovae. We decided
not to use it here to avoid getting in trouble with this paper, but
there should be little nudges as often as possible to hopefully get the
community used to the idea that maybe it's not crazy.
P. 28: 95% isn't really consistent with paragraph 3 below since they're
such different things; one is the SNe alone, the other is the SNe
combined with other things, and the shape of the regions are extremely
different in each case. People who *don't* understand that will get all
hot and bothered by the 95% CL's, since for the primary set you end up
with a 95% limit somewhere w<-1 for the supernovae alone, but much
higher when combined with the other two. "But wait, how can adding more
constraints make your data *less* limiting!?!" is what those who don't
really think through the probabilities will say. (I was listening to a
neutrino talk a month or two ago where the guy was pointing out exactly
the same sort of complaints having been raised with some limit or
another, when future measurements moved confidence regions outside
former confidence regions, and he spent time talking about probability
and such. People *will* be confused on this issue if there's an
apparent-but-not-really sore thumb like that stikcing out.) Quoting a
99% limit here both gives us a more stringent limit on what just the SNe
alone set, and don't obviously open that Pandora's box. Antoher
alternative would be to quote the SN upper limit with some w prior,
e.g. w>-1 or w>-2. (The extinction corrected 99% confidence region
extends somewhere below -80-- that's as far down as I've fit it.) I can
do whatever you want here, but I wanted to make sure you know what
you're going to see before it shows up in the next draft.
-Rob
-- --Prof. Robert Knop Department of Physics & Astronomy, Vanderbilt University robert.a.knop@vanderbilt.edu
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