Fitting the data

What you will learn

You will learn how you fit a model to COMPTEL data.

Now you are prepared to fit the model to COMPTEL data. You do this using the comlixfit script. In the example below the script is run with the debug=yes option so that the fit results are directly displayed in the terminal. comlixfit performs an iterative background fitting using the SRCLIX approach; in particuliar, the BGDLIXE method is used for background model computation.

The fit took 3 SRCLIX iterations to converge. The Crab is detected with a test statistic value of 1074.78. The fit determined the position of the gamma-ray source and the spectral power law parameters, which are the intensity at a pivot energy of 1 MeV and the spectral index. As a quality check, the fit predicted 517813.013 events in the model which is close to the observed number of 517813 events.

$ comlixfit debug=yes
Input observation definition file [obs.xml] obs_binned.xml
Input model definition file [models.xml]
Method for background computation (PHINOR|BGDLIXA|BGDLIXE) [BGDLIXE]
Output observation definition file [outobs.xml]
Output model definition file [results.xml]
...
2022-03-17T13:20:40: +====================+
2022-03-17T13:20:40: | Input observations |
2022-03-17T13:20:40: +====================+
2022-03-17T13:20:40: === GObservations ===
2022-03-17T13:20:40:  Number of observations ....: 4
2022-03-17T13:20:40:  Number of models ..........: 5
2022-03-17T13:20:40:  Number of observed events .: 517813
2022-03-17T13:20:40:  Number of predicted events : 0
2022-03-17T13:20:40:
2022-03-17T13:20:40: +============================================+
2022-03-17T13:20:40: | Iterative maximum likelihood model fitting |
2022-03-17T13:20:40: +============================================+
2022-03-17T13:20:48:  logL after iteration 1 ....: -28465.83123
2022-03-17T13:20:55:  logL after iteration 2 ....: -28466.41211 (0.58088)
2022-03-17T13:21:00:  logL after iteration 3 ....: -28466.29714 (-0.11498)
2022-03-17T13:21:09:  logL after final iteration : -28466.41290 (0.00079)
2022-03-17T13:21:09:
2022-03-17T13:21:09: +=========================================+
2022-03-17T13:21:09: | Maximum likelihood optimisation results |
2022-03-17T13:21:09: +=========================================+
2022-03-17T13:21:09: === GOptimizerLM ===
2022-03-17T13:21:09:  Optimized function value ..: -28466.413
2022-03-17T13:21:09:  Absolute precision ........: 0.005
2022-03-17T13:21:09:  Acceptable value decrease .: 0
2022-03-17T13:21:09:  Optimization status .......: converged
2022-03-17T13:21:09:  Number of parameters ......: 106
2022-03-17T13:21:09:  Number of free parameters .: 99
2022-03-17T13:21:09:  Number of iterations ......: 4
2022-03-17T13:21:09:  Lambda ....................: 0.1
2022-03-17T13:21:09:  Total number of iterations : 14
2022-03-17T13:21:09:  Maximum log likelihood ....: 28466.4129009
2022-03-17T13:21:09:  Observed events  (Nobs) ...: 517813.0
2022-03-17T13:21:09:  Predicted events (Npred) ..: 517813.012556
2022-03-17T13:21:09:  Nobs - Npred ..............: -0.012555927271
2022-03-17T13:21:09: === GModels ===
2022-03-17T13:21:09:  Number of models ..........: 5
2022-03-17T13:21:09:  Number of parameters ......: 106
2022-03-17T13:21:09: === GModelSky ===
2022-03-17T13:21:09:  Name ......................: Crab
2022-03-17T13:21:09:  Instruments ...............: all
2022-03-17T13:21:09:  Test Statistic ............: 1074.78358831939
2022-03-17T13:21:09:  Observation identifiers ...: all
2022-03-17T13:21:09:  Model type ................: PointSource
2022-03-17T13:21:09:  Model components ..........: "PointSource" * "PowerLaw" * "Constant"
2022-03-17T13:21:09:  Number of parameters ......: 6
2022-03-17T13:21:09:  Number of spatial par's ...: 2
2022-03-17T13:21:09:   RA .......................: 83.7688330639726 +/- 0.111131701366959 deg (free,scale=1)
2022-03-17T13:21:09:   DEC ......................: 21.6073511262309 +/- 0.101155131386771 deg (free,scale=1)
2022-03-17T13:21:09:  Number of spectral par's ..: 3
2022-03-17T13:21:09:   Prefactor ................: 0.00213237276990501 +/- 9.60239430063358e-05 [1e-25,infty[ ph/cm2/s/MeV (free,scale=0.002,gradient)
2022-03-17T13:21:09:   Index ....................: -2.1249932516377 +/- 0.0369030627304123 [-10,10]  (free,scale=-2,gradient)
2022-03-17T13:21:09:   PivotEnergy ..............: 1 MeV (fixed,scale=1,gradient)
2022-03-17T13:21:09:  Number of temporal par's ..: 1
2022-03-17T13:21:09:   Normalization ............: 1 (relative value) (fixed,scale=1,gradient)
2022-03-17T13:21:09:  Number of scale par's .....: 0

Note

To shorten the output, omitted lines were replaced by three dots.