From: Greg Aldering (aldering@panisse.lbl.gov)
Date: Fri May 23 2003 - 15:46:57 PDT
I don't know whether I stuck to the party line here, but I did add
some thing that I think we should say simple to support our own
method (not to attack Riess).
>From robert.a.knop@vanderbilt.edu Fri May 23 13:58:23 2003
>Date: Fri, 23 May 2003 15:58:21 -0500
>
>Changes
>
>1. The first three paragraphs of "Colors and Extinction"
>
> In this section, we discuss the limits on host-galaxy extinction we
> can set based on the measured colors of our supernovae. For the
> primary fit of our P99 analysis, extinction was estimated by comparing
> the mean host-galaxy \ebv\ values from the low- and high-redshift
> samples. Although the uncertainties on individual \ebv\ values for
> high-redshift supernovae were large, the uncertainty on the mean of
> the distribution was only 0.02 magnitudes. P99 showed that there was
> no significant difference in the mean host-galaxy reddening between
> the low and high-redshift samples of supernovae of the primary
> analysis (Fit C). This tightly constrained the systematic uncertainty
> on the cosmological results due to differences in extinction. The
> models of \citet{hat98} suggest that most SNe~Ia should be found with
> little or no host galaxy extinction. By making a cut to include only
> those objects which have small \ebv\ values, we are creating a
> subsample likely to have quite low extinction. The strength of this
> method is that it does not depend on the exact shape of the intrinsic
"\ebv\ distribution, only that most supernovae show very low
extinction. Figure~3 demonstrates that most supernovae indeed have
low-extinction, as expected from the \citet{hat98} models. Monte
Carlo simulations of our data using the \citet{hat98} extinction
distribution function and our low-extinction \mbox{$\ebv$} cuts
confirm the robustness of this approach, and further, demonstrating
that similarly low extinctions result for both low- and high-redshift
datasets despite the larger color-errors of some of our earliest
high-redshift SNe."
> \citet{rie98} used the work of \citet{hat98} differently, by applying
> a one-sided Bayesian prior to their measured \ebv\ values and
> uncertainties; this prior had zero probability for negative values of
> \ebv\, and sharply falls for positive values of \mbox{$\ebv>0.2$}
Based on the HBD P(A_B)'s I've been working with, I would say the
following. This also gives us wriggle-room in case Riess et al didn't
exactly use HBD. That is, instead of saying what their prior *was*
we say what it should have been if they did what they said they did:
"uncertainties. A prior formed from the \citet{hat98} extinction
distribution function would have zero probability for negative values
of \ebv\, a peak at \mbox{$\ebv\sim0$} with roughly 50\% of the
probability, and then an exponential tail to higher extinctions."
> magnitudes. As discussed in P99 (see the ``Fit E'' discussion, where
> P99 apply the same method to their data), when uncertainties on high-
> and low-redshift supernova colors differ, use of an asymmetric may
^^^^^
prior
> introduce bias into the cosmological results, depending on the details
> of the prior. While a prior with a tight enough peak at low
> extinction values introduces little bias (especially when low- and
> high-redshift supernovae have comparable uncertainties), it does
> reduce the apparent \ebv\ error bars on all but the most reddened
> supernovae. As we will show in Figure~ref{fig:ebvcosmofits}
> (\S~\ref{sec:cosmoparam}) the use of this prior almost completely
> eliminates the contribution of color uncertainties to size of the the
^^^ ^^^
the xxx
> cosmological confidence regions, meaning that an extinction correction
> using a sharp enough prior is much more akin to simply selecting a
> low-extinction subset than to fully performing an assumption-free
^^^^^
xxxxx
> extinction correction using the \ebv\ measurement uncertainties
> The high precision measurements of the $R$-$I$ color afforded by the
> \wfpc\ lightcurves for the new supernovae in this work allow a direct
> estimation of the host-galaxy \ebv\ color excess without any need to
> resort to a prior assumption concerning the intrinsic color-excess
^^
s
> distribution.
>
>2. Change the text on the left side, middle row of Figure 9 to
> "(Contours depend on prior used; see text)". Edit (and cut down)
> that caption so that it now reads:
>
> 68.3\%, 95.4\%, and 99.7\% confidence regions for \om\ and \ol\
> using different data subsets and methods for treating host-galaxy
> extinction corrections. The top row represents our fits to the
> low-extinction primary subset, where significantly reddened
> supernovae have been omitted and host-galaxy extinction corrections
> are not applied. The second row shows fits where extinction
> corrections have been applied using a one-sided color-excess prior.
> Note that the published contours from \citet{rie98} in this row are
> the non-dashed contours from their Fig. 6, and result from fits
> that included not only well-observed supernovae, but also
> supernovae without lightcurve color measurements (the equivalents
> to which have been omitted from the SCP sets plotted in the other
> panels), one supernova at $z=0.97$ without a spectral confirmation,
> as well as two supernovae from the P99 set. The third row shows
> fits with unbiased extinction corrections applied to our primary
> subset. The HST SNe presented in this paper show a marked
> improvement in the precision of the color measurements, and hence
> in the precision of the \om\ and \ol\ measurements when a full
> extinction correction is applied. With full and unbiased
> extinction corrections, dark energy is still required with
> \mbox{$P(\ol>0)=0.99$}.
>
> The text in the section discussing this figure didn't really go on
> about the bias, so didn't need any editing, except to remove the
> phrase "but at the expense of biasing the results" after "...hence
> apparently tightens the constraints of the cosmological confidence
> regions" (page 21). The last sentence of this paragraph no longer
> says that we do host galaxy extinction corrections in an unbiased
> manner, but just that "when host-galaxy extinction is directly and
> fully accounted for..."
This archive was generated by hypermail 2.1.4 : Fri May 23 2003 - 15:46:58 PDT