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From: Christopher Dessert <dessert@umich.edu>
Subject: Oversampling the Instrument Resolution
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From: Christopher Dessert <dessert@umich.edu>
Date: Wed, 20 Mar 2019 11:25:44 -0400
Subject: Oversampling the Instrument Resolution
To: Jan-Uwe Ness <xmmhelp@sciops.esa.int>
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Hi,

I was reviewing the documentation on specgroup and came across a sentence I
have a few questions about:

"If the number of counts in a spectrum is very high then a statistical
grouping can dramatically oversample the instrument resolution. This can
cause problems during spectral fitting because the bins are then not
completely independent."

I thought that this oversampling would not be an issue as long as the
spectrum is being forward modeled by being passed through the ARF and RMF.
This should account for the fact that infinitely thin lines are broadened
by the detector energy resolution, even if I bin at the default binning of
5 eV. Certainly, the means of each bin are not independent, but I thought
that the RMF would correct for this issue. Am I missing something? Do I
need to bin at a lower resolution? Are the errors in each bin correlated
instead?

Thanks for your help,

Chris

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<div dir=3D"ltr"><div
dir=3D"ltr"><div>Hi,</div><div><br></div><div>I
was r=
eviewing the documentation on specgroup and came across a sentence I have a=
 few questions about:<br><br>&quot;If the number of counts in a
spectrum is=
 very high then a statistical=20
grouping can dramatically oversample the instrument resolution.=20
This can cause problems
during spectral fitting because the bins are then not completely
independent.&quot;</div><div><br></div><div>I
thought that this oversamplin=
g would not be an issue as long as the spectrum is being forward modeled by=
 being passed through the ARF and RMF. This should account for the fact tha=
t infinitely thin lines are broadened by the detector energy resolution, ev=
en if I bin at the default binning of 5 eV. Certainly, the means of each bi=
n are not independent, but I thought that the RMF would correct for this is=
sue. Am I missing something? Do I need to bin at a lower resolution? Are th=
e errors in each bin correlated
instead?</div><div><br></div><div>Thanks fo=
r your help,</div><div><br></div><div>Chris<br></div></div></div>

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Reply 1

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From: Rosario Gonzalez Riestra <xmmhelp@sciops.esa.int>
To: dessert@umich.edu
Subject: Re: Oversampling the Instrument Resolution (PR#84794)
Date: Thu Mar 21 10:46:30 2019
Dear Chris,

A minimum level of spectral rebinning is always required to avoid
oversampling the intrinsic resolution of the instrument. It can
be shown (from Shannon and Nyquist theorems) that the optimal bin
sampling is approx 1/3 of the instrumental FWHM, for spectra with
a high number of counts. No information is lost if this rebin is used.
Also, oversampling the spectral resolution wouldincrease the probability of
falsely accepting wrong models.

Regrads,


Rosario Gonzalez-Riestra
XMM-SOC User Support Group

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