Caution about chi^2 estimation of PI spectra

From: Koji Mori (mori@leo.astro.psu.edu)
Date: Mon Mar 05 2001 - 17:50:36 EST


Dear chandra-users,

If you are estimating the parameters of a model by the chi^2 value, I
recommend that you take the following into account.

A month ago, a caveat about PI spectra was posted at
http://asc.harvard.edu/ciao/caveats/acis_pi.html.
The problem and its cause were described in it.

Although it was thought that only a few observers who have extremely high
statistics would be affected, I know of some examples where the effect of
the problem to the chi^2 value is not negligible even in the case of
relatively low statistics (e.g., 1400 counts), especially for PI spectra
with full resolution (1024 bins).

I show a simple solution of it using ftools,

        fcalc input.fits tmp.fits energy "energy + GAIN*(random()-0.5)"
        fcalc tmp.fits output.fits pi "(int) (energy/14.6) + 1"

Please be careful that you have to determine the value of GAIN by
yourself. If your source is within a single FEF region, you can easily
derive it from the gain file or fitting "PHA vs ENERGY" with a linear
function. However, if your source covers multiple FEF regions, you have to
choose the GAIN value more carefully. Changing the GAIN value every FEF
region is best but perhaps not realistic. It will be safe to choose the
biggest value among your FEF regions, though I don't know how different
the GAIN values are.

Based on my experience, it's a good idea to compare the parameters and the
chi^2 values before and after adding in randomization if the chi^2
estimation of model parameters is key to your paper.

Regards,
Koji Mori
-------------------------------------------------------------
                         Koji Mori
                    mori@astro.psu.edu

Department of Astronomy & Astrophysics, 525 Davey Laboratory
   Penn State University, University Park, PA 16802, U.S.A.

           Phone:(1)-814-863-0182, Fax:(1)-814-863-3399
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