Re: Chi2 calculation for rebinned spectra in ISIS

Hi Maria,

It looks like dmgroup adds the errors of the grouped bins in quadrature. I believe ISIS defaults to Poisson errors upon rebinning. If you do:

set_rebin_error_method(1,"quadsum");
rebin_data(1,25);

and set the fit parameters to your best fit in XSPEC, do you get the same chi^2 in ISIS?

Cheers,

Joey

On Apr 30, 2014, at 3:48 AM, María Díaz Trigo <mdiaztri_at_email.domain.hidden
> Hi...
> 
> thanks to all of you for your advice. See some details below:
> 
> - I haven't added any systematic error
> - I get the same result whether I rebin the spectra within ISIS or outside of ISIS
> - For rebinning outside of ISIS I use the CIAO task dmgroup and set:
> 
>   pset dmgroup grouptype=NUM_CTS 
>   pset dmgroup grouptypeval=25
>   pset dmgroup xcolumn=channel
>   pset dmgroup ycolumn=counts
> 
> - For rebinning inside ISIS I use 'rebin_data(1,25);'
> - I have checked that the problem is not related to finding different local minima when fitting with XSPEC and ISIS
> 
> Now, going to the error per bin:
> 
> - I used get_data_counts in ISIS and I get indeed an error of sqrt(num_cts) for each value, which seems OK. 
> These values are also the ones that appear in the data fits file in columns grp_data and grp_stat_err. So 
> it seems that XSPEC doesn't take these values and calculates them in a different way, otherwise there shouldn't be any
> difference...
> 
> - So maybe the problem is how xspec interprets a file created by dmgroup: I see a column called stat_err in the file, which
> is not sqrt(num_cts). I presume that xspec is adding that error to whatever error is calculated on the number of counts and
> therefore the errors are bigger than they should (and consequently the chi2 smaller)...
> 
> Does this make sense?
> 
> Cheers,
> 
> Maria
> 
> From: Michael Nowak [mnowak_at_email.domain.hidden> Sent: 29 April 2014 16:54
> To: María Díaz Trigo
> Cc: isis-users_at_email.domain.hidden> Subject: Re: isis-users: Chi2 calculation for rebinned spectra in ISIS 
> 
> 
> On Apr 29, 2014, at 5:44 AM, María Díaz Trigo <mdiaztri_at_email.domain.hidden> 
>> I have realised that the chi2 value for rebinned spectra is very different when calculated by ISIS and XSPEC. The chi2 is exactly the same when I use non-binned spectra, so the difference must arise with the way of calculating errors after rebinning.
>> 
>> I am using the default fitting method (which seems to be the same for XSPEC and ISIS) and rebin the HEG spectra to have a minimum of 25 cts/bin. Before rebinning, a simple power law fit gives me a chi2 of 838.37 for 2362 dof both in ISIS and XSPEC. After rebinning, I get:
>> 
>> XSPEC: Chi2 of 217.90 (460) 
>> ISIS: Chi2 of 420.46 (460)
>> 
>> So the difference is almost a factor of two, and the parameters of the fit are also different. 
>> 
>> Do you know why am I getting such a difference?
> 
> Hi Maria-
> 
> We'd need a few more details, but here's where the differences can arise:
> 
> * If you read in a spectral file into ISIS and *don't* rebin, then the error will be
> whatever is in the error column of the file, and this will depend upon how you
> made the file.  (This is also true in ISIS if one uses define_counts to create
> the data – it defaults to whatever you set the err column to be originally.)
> 
> * The one modification to the above is that ISIS will set a lower limit on the error
> via the Minimum_Stat_Err variable (which defaults to 1, *unless* you are using
> my .isisrc routines, in which case I set it to 1.e-30).  So, any bins with 0 counts
> in them very well might be an issue, and be treated differently in ISIS vs. XSPEC.
> 
> * If you rebin the data *within* ISIS, then it follows whatever was set by 
> set_rebin_error_method, which defaults to poisson == sqrt(grouped_counts),
> with the caveat that Minimum_Stat_Err still applies.
> 
> * Errors are further modified by whether or not systematic errors were set.  In 
> ISIS, they will only be applied if you set them within the program, regardless of
> what the spectral file says.
> 
> In the end, ISIS and XSPEC should always give the same answer to several
> decimal places, once we verify that things have been set up the same.
> (I honestly don't remember what the defaults are for XSPEC when it comes
> to errors – I think it also defaults to what's in the error column of the file,
> which possibly might not be following sqrt(summed counts), depending upon
> how the binned file was made.) 
> 
> Did you bin the data outside of ISIS and then read it in, or is this a case of
> binning one outside for XSPEC, and one inside for ISIS?  
> 
> The ISIS function get_data_counts will retrieve the data into a structure, and
> then you can just see directly what you have for the value and errors for the
> data.  That would likely help you figure out where any differences are coming
> from.  
> 
> You can feel free to directly send me data & script, and I can help explain further
> based upon what you did.
> 
> -Mike
> 
> 
> 

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Dr. Joey Neilsen
Einstein Postdoctoral Fellow
Institute for Astrophysical Research, Boston University
725 Commonwealth Avenue, 416D
Boston, MA 02215, USA

Email: neilsenj_at_email.domain.hiddenWeb: people.bu.edu/neilsenj
Phone: (617) 353-1533
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