...
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
Prefactor |
|
| Index |
|
| |
---|---|---|---|---|---|---|
true +/- err. est.value | MC dist | true +/- err. est. | KS prob | true value | MC dist | KS probMC |
27.00 +/- 1.86 | 27.21 +/- 1.92 | 4.14e-03 | -2.19 +/- 0.05 | -2.16 +/- 0.06 | 1.59e-26 |
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
Prefactor |
|
| Index |
|
|
---|---|---|---|---|---|
true +/- err. est.value | MC dist | KS prob | true +/- err. est.value | MC dist | KS prob |
27.00 +/- 1.78 | 28.19 +/- 1.84 | 3.55e-62 | -2.19 +/- 0.05 | -2.22 +/- 0.05 | 1.39e-60 |
Markov Chain Monte Carlo (MCMC)
...
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
...
Extragalactic Diffuse
The ROI file.
Prefactor |
|
| Index |
|
| |
---|---|---|---|---|---|---|
true +/- err. est.value | MC dist | true +/- err. est. | KS prob | true value | MC dist | KS probMC |
1.45 | 1.48 +/- 0.06 | 1.48 +/- 0.0602e-55 | -2.10 +/- 0.03 | -2.10 +/- 0.03 | 5.79e-08 |