Thursday, July 14, 2005


Pat Broos reported a discontinuity in Cstat when running under Solaris with a very weak source and background. Craig spotted this as round-off error when solving the quadratic in the case where b^2 >> ac. Fixed this using the algorithm from NR. Also explicitly handled the special cases of zero source or background counts in a channel. I don't think this latter changed any results.

Note that in the very weak source limit Cstat appears to exhibit bias in some circumstances ie the best fit does not appear to be correct when doing a plot icounts. Cstat with background is a profile likelihood which is well known in the statistics literature to exhibit bias in the low sample limit. A practical partial solution appears to be to run grppha with group min 1 to ensure that every bin has at least one count. The statistics literature does offer corrections to the profile likelihood but these appear to be algebraically very complex in this case.

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