Both are numerical integrals of the same quantity, so duplication represents a check of both methods: MC is more reliable, necessary to validate analytic.
Analytic is much faster, allows study of effect of assumptions, dependence on subsets (front vs back, energy, changing source parameters, PSF)
For a point source, and assumed PSF, the measurement error from a maximum likelihood fit is easily predicted. If P(x,y) is the normalized probability distribution describing angular deviations, and there are N signal photons, then the projected resolution* is
*This is derived in the Jay Orear memo on statistics, see http://nedwww.ipac.caltech.edu/level5/Sept01/Orear/frames.html
The probability function has to be modified, with the addition of the constant term, parameterized by the ratio of the number of background in 2 2 to the total signal, denoted by b. The result:
Bottom line: x =18 arcsec for T live =1 year. The corresponding radius is 1.5 times this, or 27 arcsec.
Background has little effect
The distribution of the inverse variance peaks at 30 GeV: as there are only 58 events expected above 10 GeV, the result is subject to statistical fluctuations.
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