From: Chris Lidman (clidman@eso.org)
Date: Thu Dec 11 2003 - 05:00:24 PST
Hi Ariel,
I will not continue the debate until I have a clearer understanding
of
the implications of our procedure.
As I was reading through the paper last night, another idea occurred
to me.
The I band fit requires five parameters, however, we have fewer data
points
than paramters.
Have you ever thought of using the correlations between parameters or
perhaps limiting the range over which parameters can vary to try and
reduce the number of parameters.
For example, one could limit the range of parameter space with
t_max =-1 +/- 2 days
t_sec = f(s_B), for 00fr, t_sec=29 +/- 2
M_sec < M_max
Cheers, Chris.
Ariel Goobar wrote:
> Hi Chris,
> I might be missing your point (sorry!), but yet, I fail to see the
> essense
> of your argument. Consider the optical lightcurve fits that we have
> been doing all along with eg SNMINUIT. There are several parameters
> involved, correlated in various manners: peak mag, time of max,
> stretch + at some point we also had some parameter to extrapolate
> the early rise-time behaviour, and we also combine data in more
> than one band. There are more parameters involved w.r.t the
> lightcurve shape + (possible priors), yet, I don't think we ever
> considered doing anything different than a chi2 minimization to select
> our best.
>
> Cheers,
> Ariel
>
>>>
>>> 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.
>>
>>
>>
>
> --
> ___________________________________________________________________
> Ariel Goobar (www.physto.se/~ariel)
> Department of Physics, Stockholm University
> AlbaNova University Center, SE-106 91 Stockholm, SWEDEN
> tel: +46 8 55378659 fax: +46 8 55378601
This archive was generated by hypermail 2.1.4 : Mon Dec 15 2003 - 17:08:57 PST