From: Chris Lidman (clidman@eso.org)
Date: Wed Dec 10 2003 - 18:19:15 PST
Hi Ariel,
Some additional comments ...
Ariel Goobar wrote:
> Hi Chris et al,
>
> Serena is working on finishing some important details of
> I-band paper: redoing the LC fits with the Sofie J-band
> K-corrections for the one point for 99Q (thanks Chris for the
> transmission
> curves!) and recomputing the
> chisquare for the color-color diagrams in section 6 corresponding to
> Fig
> 17, where we concluded the numbers in the text are not really what we
> want to use to test the IG dust hypothesis. In the mean time,
> I thought I would comment on your comment below, with respect to the
> way
> that the systematic uncertainty on trhe high-z LC fit is done, see
> below.
>>>
>>> Moreover given the large difference in chisq between the best fit
>>> one and
>>> the next (at least for 2000fr and 1999ff), I do not think is really
>>> fair
>>> to average together the results up to chisq_min+3.
>>> As you said, this will not change the results anyway, but I don't
>>> think
>>> averaging results from "worse" fits, would give a more robust
>>> estimate of
>>> the maximum.
>>>
>>
>> I'm not sure and I'd like to explore this point further. Ask yourself
>> the following question. Why would you use one sample to compute the
>> first moment of a distribution and then a larger sample to compute a
>> higher order moment. This is what you have done. You have used one
>> point (the one with the lowest chi-sqaure) to compute the "average",
>> but you use a larger sample (the ones with chisq_min+3) to compute the
>> RMS. I'd argue that you should the same sample to do both. I.e
>> compute the mean, median, standard deviation) from the same sample.
>
> Let me give you another analogy, that I think is closer to what
> Serena has done. Imagine that, instead of using the chi2
> minimum to give our best fit omega-lambda cosmology, we would do
> what you propose: compute the "mean" cosmology from all the
> solutions that are within chi2_min +3. Wouldn't that be a very
> odd procedure? The "orthodox" thing is to find your chi2 minimum
> and establish your parameter uncertainty by looking at chi2_min +- 1,
> for the 68% CL 1-dim case. This is exactly how Serena is trying
> to assess the SYSTEMATIC uncertainty (note, not RMS/STATISTICAL
> uncertainty) from her template "grid search" fit to the data.
>
This is true when you are able to freely explore chi-square space by
varying the cosmological parameters in a systematic, semi-continuous
fashion.
The case of the lightcurve fits to high-z SNe is more complicated,
because
one is minimising a chi-sq square space that includes one
continuous parameter (the normalisation of the lightcurve) and another
parameter which is the lightcurve shape. This second one is unusual and
it
is not clear if your analogy (or mine) applies in this case. Clearly,
more
thought is required.
Cheers, Chris.
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