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Error estimates for any single fit are given by taking the square root of the diagonal elements of the covariance matrix, which in turn is estimated as the inverse Hessian of the -log-likelihood. Note that the definition of the confidence interval corresponds to a specified change in the log-likelihood along a given direction in parameter space. The estimates obtained from the inverse Hessian are only accurate insofar as the likelihood surface at the local minimum can be accurately represented as a quadratic function of the model parameters. The error estimates reported below are averaged over each set of Monte Carlo trials.

Binned Analysis

Counts maps for the Crab_Pulsar, the three anticenter sources, and extragalactic diffuse tests are prepared for the following geometry:
E _min = 30, E _max = 3e5 MeV, 39 bins, logrithmically spaced
RA _center = 83 ^o, eighty 0.5 ^o pixels
Dec _center = 22 ^o, eighty 0.5 ^o pixels

A single point source: Crab_Pulsar

Three strong sources in the Galactic anticenter region: PKS 0528+134, Crab, Geminga

Here is a FITS image of the count map, summed over energies, used in these fits.

• PKS0528+134
  

  Prefactor			Index
  true value	MC dist	KS prob	true value	MC dist	KS prob	true +/- err. est.	MC	true +/- err. est.	MC
  13.65 +/- 1.68	14.37 +/- 1.70	6.31e-25	-2.46 +/- 0.09	-2.55 +/- 0.13	1.87e-73

• Crab
  

  Prefactor			Index
  true +/- err. est.value	MC dist	KS prob	true +/- err. est.value	MC dist	KS prob
  27.00 +/- 2.14	26.74 +/- 2.19	9.48e-03	-2.19 +/- 0.05	-2.15 +/- 0.07	3.61e-52

• Geminga
  

  Prefactor			Index
  true +/- err. est.value	MC dist	KS prob	true +/- err. est.value	MC dist	KS prob
  23.29 +/- 1.73	23.62 +/- 1.88	1.96e-07	-1.66 +/- 0.02	-1.66 +/- 0.04	1.69e-02

Unbinned Analysis

These analyses use this ROI file.

Crab_Pulsar

Markov Chain Monte Carlo (MCMC)

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PKS 0528+134, Crab, & Geminga

• PKS0528p134
  

  Prefactor			Index
  true +/- err. est.value	MC dist	KS prob	true +/- err. est.value	MC dist	KS prob
  13.65 +/- 1.76	14.62 +/- 1.75	3.13e-40	-2.46 +/- 0.11	-2.52 +/- 0.11	5.13e-40

• Crab
  

  Prefactor			Index
  true valuetrue +/- err. est.	MC dist	true +/- err. est.	KS prob	true value	MC dist	KS probMC
  27.00 +/- 2.02	28.10 +/- 2.03	7.68e-42	-2.19 +/- 0.05	-2.22 +/- 0.06	1.63e-42

• Geminga
  

  Prefactor			Index
  true +/- err. est.value	MC dist	KS prob	true +/- err. est.value	MC dist	KS prob
  23.29 +/- 1.68	24.38 +/- 1.74	4.84e-59	-1.66 +/- 0.03	-1.68 +/- 0.03	4.37e-58

MCMC results for a single trial

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Extragalactic Diffuse

The ROI file.