From: Greg Aldering (aldering@panisse.lbl.gov)
Date: Sun May 18 2003 - 11:47:10 PDT
>From robert.a.knop@vanderbilt.edu Sun May 18 11:04:04 2003
>To: Greg Aldering <aldering@panisse.lbl.gov>, Saul Perlmutter <saul@lbl.gov>
>
>On Sun, May 18, 2003 at 12:47:16PM -0500, Robert A. Knop Jr. wrote:
>> > 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.
>>
>> 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.
>
>OK, thinking about this more--
>
>Of course, as has been previously noted, we *are* using a prior on our
>low-extinction subset, that is E(B-V)=0+-0. This prior has the
>advantage of being unbiased even if your error bars are different at low
>and high redshift. (Sort of; in fact, there is an implicit bias,
>because if one set has worse error bars, it will keep more mildly
>extincted supernove than the other set. The prior doesn't *impose* a
>bias the way the Riess one does)
>
>If we really want to be self-consistent and run with this-- basically
>doing what you say, we've tested this assumption and it sure seems to
>hold-- then we should use *no* host galaxy extinction systematic
>whatsoever on the low-extinction subset. If somebody cares about
>extinction, then they look at Fit 6.
>
>This approach may actually make the most sense.
>
>Thoughts?
>
Yes, I've been mulling this over too, and I think the concept you have
outlined is the way to go. The key aspect that is different than what
Riess et al does is that we don't need to know the functional form of
the prior, and as you say, we don't bias our fits - at least not in the
same way.
Elaborating further, I would also say that our assumption is even more
generous than E(B-V)=0+-0. It is more like:
| <P(A_B,z=low | E(B-V) < XX)> - <P(A_B,z=high | E(B-V) < XX)> | << stat error
where P(A_B) is the extinction distribution, and XX indicates the reddening
cut that makes the low-extinction subsample, and < > indicates the mean of
the distribution. I put in the "<< stat error" to indicate the general case
that people really only worry about systematics if they think the size of the
systematic is becoming appreciable relation to the statistical error.
Let's see if others are on board with this.
- Greg
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