RE: Chi2 calculation for rebinned spectra in ISIS

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.hiddenSent: 29 April 2014 16:54
To: María Díaz Trigo
Cc: isis-users_at_email.domain.hiddenSubject: 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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