Re: 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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