Test statistic for FG decomposition

[fzeiser]

Issue by fzeiser Wednesday Aug 28, 2019 at 08:10 GMT Originally opened as https://github.com/oslocyclotronlab/ompy/issues/28

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There are some question as to how to implement the test statistics for the decomposition of the fist generation matrix into nld and gsf/transmission coefficient.

• How to deal with low number of counts? Sometimes the measured spectrum may have few counts in some region, or even 0 counts. Using a chi2 with sigma^2=N i) doesn't work (1/N for N=0) and ii) maybe doesn't make much sense.
• We could try some other statistics like C-stat? See eg https://asd.gsfc.nasa.gov/XSPECwiki/low_count_spectra, and http://arxiv.org/abs/1707.09202v1
• How to deal with the regions where we "cut away" negative counts in unfolding/fg-method?

Some reasons we may have few/zero counts: Artificial:

• unfolding/fg-method error: negative counts that are set to zero

Actual:

• Larger gaps between first levels -> NLD is zero -> Should appear as diagonal ridges in the FG spectra (not sure how unfolding works on them)