Bug #1503

Pull distributions of stacked analysis look shifted

Added by Buehler Rolf over 7 years ago. Updated about 7 years ago.

Status:ClosedStart date:07/03/2015
Priority:NormalDue date:
Assigned To:Knödlseder Jürgen% Done:

100%

Category:-
Target version:1.0.0
Duration:

Description

I modyfied cspull to handle stacked observations. Using it to simulate and fit three observations, containing the Crab and a CTA background as sources, results in the following pull distributions:




The seems to be an atribution of source photons to the background. The used observations and source models are attached. I will push the modified cspull after some small further improvements to it.

Pull_BackgroundModel_Index.png (41.3 KB) Buehler Rolf, 07/03/2015 10:03 AM

Pull_BackgroundModel_Prefactor.png (42.8 KB) Buehler Rolf, 07/03/2015 10:03 AM

Pull_Crab_Index.png (38 KB) Buehler Rolf, 07/03/2015 10:03 AM

Pull_Crab_Prefactor.png (39.1 KB) Buehler Rolf, 07/03/2015 10:03 AM

obs.xml Magnifier (1.79 KB) Buehler Rolf, 07/03/2015 10:05 AM

crab.xml Magnifier (1.13 KB) Buehler Rolf, 07/03/2015 10:05 AM

cspull_input.png (25.6 KB) Buehler Rolf, 07/03/2015 10:20 AM

cspull_input.png (27.4 KB) Buehler Rolf, 07/03/2015 10:30 AM

cspull_input.png (36.3 KB) Buehler Rolf, 07/03/2015 12:34 PM

Pull_BackgroundModel_Index.png (41.8 KB) Buehler Rolf, 07/03/2015 12:34 PM

Pull_BackgroundModel_Prefactor.png (38.9 KB) Buehler Rolf, 07/03/2015 12:34 PM

Pull_Crab_Index.png (38 KB) Buehler Rolf, 07/03/2015 12:34 PM

Pull_Crab_Prefactor.png (39 KB) Buehler Rolf, 07/03/2015 12:34 PM

pull_b20_prefactor.png (41.3 KB) Knödlseder Jürgen, 07/03/2015 04:09 PM

pull_b20_index.png (39.7 KB) Knödlseder Jürgen, 07/03/2015 04:09 PM

pull_b40_index.png (39.8 KB) Knödlseder Jürgen, 07/03/2015 04:09 PM

pull_b40_prefactor.png (41.1 KB) Knödlseder Jürgen, 07/03/2015 04:09 PM

pull_b40_bkg_prefactor.png (44.7 KB) Knödlseder Jürgen, 07/03/2015 04:09 PM

pull_b40_bkg_index.png (43.7 KB) Knödlseder Jürgen, 07/03/2015 04:09 PM

pull_b20_prefactor_binsz002.png (41.3 KB) Knödlseder Jürgen, 07/03/2015 06:04 PM

pull_b20_index_binsz002.png (40.1 KB) Knödlseder Jürgen, 07/03/2015 06:04 PM

pull_b20_id_index.png (39.9 KB) Knödlseder Jürgen, 07/03/2015 06:41 PM

pull_b20_id_prefactor.png (41.2 KB) Knödlseder Jürgen, 07/03/2015 06:41 PM

pull_b20_single_prefactor.png (41.3 KB) Knödlseder Jürgen, 07/03/2015 06:46 PM

pull_b20_single_index.png (40 KB) Knödlseder Jürgen, 07/03/2015 06:46 PM

residual.fits.gz (5.72 MB) Knödlseder Jürgen, 07/03/2015 11:26 PM

new_binsz005_b20_bkg_index.png (44.1 KB) Knödlseder Jürgen, 07/04/2015 01:03 AM

new_binsz005_b20_bkg_prefactor.png (45.5 KB) Knödlseder Jürgen, 07/04/2015 01:03 AM

new_binsz005_b20_index.png (48 KB) Knödlseder Jürgen, 07/04/2015 01:03 AM

new_binsz005_b20_prefactor.png (41.8 KB) Knödlseder Jürgen, 07/04/2015 01:03 AM

new_binsz002_b20_bkg_index.png (44.2 KB) Knödlseder Jürgen, 07/04/2015 01:55 AM

new_binsz002_b20_bkg_prefactor.png (45.2 KB) Knödlseder Jürgen, 07/04/2015 01:55 AM

new_binsz002_b20_index.png (40.2 KB) Knödlseder Jürgen, 07/04/2015 01:55 AM

new_binsz002_b20_prefactor.png (49.1 KB) Knödlseder Jürgen, 07/04/2015 01:55 AM

plaw_binsz002_b10_index.png (43.9 KB) Knödlseder Jürgen, 08/21/2015 03:08 PM

plaw_binsz002_b10_prefactor.png (45.3 KB) Knödlseder Jürgen, 08/21/2015 03:08 PM

plaw_binsz002_b15_index.png (43.9 KB) Knödlseder Jürgen, 08/21/2015 03:08 PM

plaw_binsz002_b15_prefactor.png (45.2 KB) Knödlseder Jürgen, 08/21/2015 03:08 PM

plaw_binsz002_b20_index.png (43.7 KB) Knödlseder Jürgen, 08/21/2015 03:08 PM

plaw_binsz002_b20_prefactor.png (45 KB) Knödlseder Jürgen, 08/21/2015 03:08 PM

plaw_binsz002_b30_index.png (43.5 KB) Knödlseder Jürgen, 08/21/2015 03:08 PM

plaw_binsz002_b30_prefactor.png (44.8 KB) Knödlseder Jürgen, 08/21/2015 03:08 PM

plaw_binsz002_b40_index.png (43.7 KB) Knödlseder Jürgen, 08/21/2015 03:08 PM

plaw_binsz002_b40_prefactor.png (44.6 KB) Knödlseder Jürgen, 08/21/2015 03:08 PM

Pull_backgroundmodel_index Pull_backgroundmodel_prefactor Pull_crab_index Pull_crab_prefactor Cspull_input Cspull_input Cspull_input Pull_backgroundmodel_index Pull_backgroundmodel_prefactor Pull_crab_index Pull_crab_prefactor Pull_b20_prefactor Pull_b20_index Pull_b40_index Pull_b40_prefactor Pull_b40_bkg_prefactor Pull_b40_bkg_index Pull_b20_prefactor_binsz002 Pull_b20_index_binsz002 Pull_b20_id_index Pull_b20_id_prefactor Pull_b20_single_prefactor Pull_b20_single_index New_binsz005_b20_bkg_index New_binsz005_b20_bkg_prefactor New_binsz005_b20_index New_binsz005_b20_prefactor New_binsz002_b20_bkg_index New_binsz002_b20_bkg_prefactor New_binsz002_b20_index New_binsz002_b20_prefactor Plaw_binsz002_b10_index Plaw_binsz002_b10_prefactor Plaw_binsz002_b15_index Plaw_binsz002_b15_prefactor Plaw_binsz002_b20_index Plaw_binsz002_b20_prefactor Plaw_binsz002_b30_index Plaw_binsz002_b30_prefactor Plaw_binsz002_b40_index Plaw_binsz002_b40_prefactor

Recurrence

No recurrence.

History

#1 Updated by Buehler Rolf over 7 years ago

#2 Updated by Buehler Rolf over 7 years ago

The input parameters are shown in the image shown below. Note that the expcube, psfcube, bkgcube are done with the same binning as the ctscube, which is not efficient, but avoids user errors.

#3 Updated by Buehler Rolf over 7 years ago

#4 Updated by Buehler Rolf over 7 years ago

I fixed a bug in my cspull version. This changed the distributions, but they are now even more offset for the background (I updated the figures, so the plots above show the correct plots). I will push my cspull modifications into devel.

#5 Updated by Knödlseder Jürgen over 7 years ago

I integrated the modified cspull script into ctools. Please note that I have removed the expcube, psfcube and bkgcube parameters from cspull as they were in fact not used. You need to clean-up your pfiles folder so that you don’t have an old version with these parameters lurking around.

It turned out that the background cube model indeed had the livetime correction twice. The background cube rates are counts/livetime, but then there was an additional correction in the GCTAModelCubeBackground code. I removed that. The background pulls are now much more reasonable.

Below a comparison of 20 energy bins (top row) to 40 energy bins (bottom row). This does not seem to impact the results.

I also provide for reference the background model spectral parameter pull histograms for 40 bins.

Note that the fitting shows always a residual in Npred. Not clear whether this is a bad Npred computation, or whether this is actually a problem in the fit (which seems to converge):

2015-07-03T14:10:40: +=================================+
2015-07-03T14:10:40: | Maximum likelihood optimisation |
2015-07-03T14:10:40: +=================================+
2015-07-03T14:10:41:  >Iteration   0: -logL=47448.077, Lambda=1.0e-03
2015-07-03T14:10:42:  >Iteration   1: -logL=47447.780, Lambda=1.0e-03, delta=0.298, max(|grad|)=7186008816.917294 [Index:7]
2015-07-03T14:10:43:  >Iteration   2: -logL=47447.779, Lambda=1.0e-04, delta=0.000, max(|grad|)=7186004339.309735 [Index:7]
2015-07-03T14:10:43:  
2015-07-03T14:10:43:  +==================+
2015-07-03T14:10:43:  | Curvature matrix |
2015-07-03T14:10:43:  +==================+
2015-07-03T14:10:43:  === GMatrixSparse ===
2015-07-03T14:10:43:   Number of rows ............: 10
2015-07-03T14:10:43:   Number of columns .........: 10
2015-07-03T14:10:43:   Number of nonzero elements : 16
2015-07-03T14:10:43:   Number of allocated cells .: 528
2015-07-03T14:10:43:   Memory block size .........: 512
2015-07-03T14:10:43:   Sparse matrix fill ........: 0.16
2015-07-03T14:10:43:   Pending element ...........: 0
2015-07-03T14:10:43:   Fill stack size ...........: 0 (none)
2015-07-03T14:10:43:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T14:10:43:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T14:10:43:   0, 0, 188.146, -286.823, 0, 0, 1.12635e+06, 3.47759e+06, 0, 0
2015-07-03T14:10:43:   0, 0, -286.823, 8616.04, 0, 0, -2.7315e+07, -9.1871e+07, 0, 0
2015-07-03T14:10:43:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T14:10:43:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T14:10:43:   0, 0, 1.12635e+06, -2.7315e+07, 0, 0, 1.63675e+17, 5.60271e+17, 0, 0
2015-07-03T14:10:43:   0, 0, 3.47759e+06, -9.1871e+07, 0, 0, 5.60271e+17, 1.93156e+18, 0, 0
2015-07-03T14:10:43:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T14:10:43:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T14:10:43: 
2015-07-03T14:10:43: +=========================================+
2015-07-03T14:10:43: | Maximum likelihood optimization results |
2015-07-03T14:10:43: +=========================================+
2015-07-03T14:10:43: === GOptimizerLM ===
2015-07-03T14:10:43:  Optimized function value ..: 47447.779
2015-07-03T14:10:43:  Absolute precision ........: 0.005
2015-07-03T14:10:43:  Acceptable value decrease .: 2
2015-07-03T14:10:43:  Optimization status .......: converged
2015-07-03T14:10:43:  Number of parameters ......: 10
2015-07-03T14:10:43:  Number of free parameters .: 4
2015-07-03T14:10:43:  Number of iterations ......: 2
2015-07-03T14:10:43:  Lambda ....................: 1e-05
2015-07-03T14:10:43:  Maximum log likelihood ....: -47447.779
2015-07-03T14:10:43:  Observed events  (Nobs) ...: 39586.000
2015-07-03T14:10:43:  Predicted events (Npred) ..: 37661.415 (Nobs - Npred = 1924.59)

#6 Updated by Knödlseder Jürgen over 7 years ago

There is a dependence on the size of the counts map. The original runs were for a 100 x 100 pixel map with 0.05 deg pixels, hence covering an area of 5 x 5 deg.

I tried a smaller map with a binsize of 0.02 deg and still 100 x 100 pixels, covering 2 x 2 deg.

There is still an issue with the Npred value:

2015-07-03T16:02:29: +=========================================+
2015-07-03T16:02:29: | Maximum likelihood optimization results |
2015-07-03T16:02:29: +=========================================+
2015-07-03T16:02:29: === GOptimizerLM ===
2015-07-03T16:02:29:  Optimized function value ..: 16666.857
2015-07-03T16:02:29:  Absolute precision ........: 0.005
2015-07-03T16:02:29:  Acceptable value decrease .: 2
2015-07-03T16:02:29:  Optimization status .......: converged
2015-07-03T16:02:29:  Number of parameters ......: 10
2015-07-03T16:02:29:  Number of free parameters .: 4
2015-07-03T16:02:29:  Number of iterations ......: 15
2015-07-03T16:02:29:  Lambda ....................: 0.01
2015-07-03T16:02:29:  Maximum log likelihood ....: -16666.857
2015-07-03T16:02:29:  Observed events  (Nobs) ...: 16452.000
2015-07-03T16:02:29:  Predicted events (Npred) ..: 15032.236 (Nobs - Npred = 1419.76)

#7 Updated by Knödlseder Jürgen over 7 years ago

  • Status changed from New to In Progress
  • Assigned To set to Knödlseder Jürgen
  • % Done changed from 0 to 10

#8 Updated by Knödlseder Jürgen over 7 years ago

I did another test without offset between the runs, hence 3 observations with the same pointing (Crab) and an ROI of 5 deg.

I used 20 bins in energy and 100 x 100 pixels of 0.05 deg/pixel, i.e. a 5 x 5 deg counts map. Below the resulting pull distribution. There is still the bias in the index. This seems to be inherent to large maps.

The Npred value is also too large:

2015-07-03T16:23:52: === GOptimizerLM ===
2015-07-03T16:23:52:  Optimized function value ..: 10240.417
2015-07-03T16:23:52:  Absolute precision ........: 0.005
2015-07-03T16:23:52:  Acceptable value decrease .: 2
2015-07-03T16:23:52:  Optimization status .......: converged
2015-07-03T16:23:52:  Number of parameters ......: 10
2015-07-03T16:23:52:  Number of free parameters .: 4
2015-07-03T16:23:52:  Number of iterations ......: 6
2015-07-03T16:23:52:  Lambda ....................: 0.1
2015-07-03T16:23:52:  Maximum log likelihood ....: -10240.417
2015-07-03T16:23:52:  Observed events  (Nobs) ...: 45473.000
2015-07-03T16:23:52:  Predicted events (Npred) ..: 43741.983 (Nobs - Npred = 1731.02)

#10 Updated by Knödlseder Jürgen over 7 years ago

For comparison, I did the same simulation, but now using a classical binned analysis. The difference is now that the response information is taken from the original IRFs, and not the stacked versions. The results show the same shifts, but the Npred number is now correct. Note that the fit gradients are also much smaller.

I’m wondering whether there are in fact two different problems to understand.

2015-07-03T16:46:08: +=================================+
2015-07-03T16:46:08: | Maximum likelihood optimisation |
2015-07-03T16:46:08: +=================================+
2015-07-03T16:46:09:  >Iteration   0: -logL=14855.667, Lambda=1.0e-03
2015-07-03T16:46:09:  >Iteration   1: -logL=14851.929, Lambda=1.0e-03, delta=3.738, max(|grad|)=4.217249 [Index:7]
2015-07-03T16:46:10:  >Iteration   2: -logL=14851.928, Lambda=1.0e-04, delta=0.001, max(|grad|)=0.027799 [Index:3]
2015-07-03T16:46:10:  
2015-07-03T16:46:10:  +==================+
2015-07-03T16:46:10:  | Curvature matrix |
2015-07-03T16:46:10:  +==================+
2015-07-03T16:46:10:  === GMatrixSparse ===
2015-07-03T16:46:10:   Number of rows ............: 10
2015-07-03T16:46:10:   Number of columns .........: 10
2015-07-03T16:46:10:   Number of nonzero elements : 16
2015-07-03T16:46:10:   Number of allocated cells .: 528
2015-07-03T16:46:10:   Memory block size .........: 512
2015-07-03T16:46:10:   Sparse matrix fill ........: 0.16
2015-07-03T16:46:10:   Pending element ...........: 0
2015-07-03T16:46:10:   Fill stack size ...........: 0 (none)
2015-07-03T16:46:10:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T16:46:10:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T16:46:10:   0, 0, 259.335, -320.444, 0, 0, 82.9803, -147.697, 0, 0
2015-07-03T16:46:10:   0, 0, -320.444, 10997.4, 0, 0, 264.36, -593.486, 0, 0
2015-07-03T16:46:10:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T16:46:10:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T16:46:10:   0, 0, 82.9803, 264.36, 0, 0, 35867.2, -58400.5, 0, 0
2015-07-03T16:46:10:   0, 0, -147.697, -593.486, 0, 0, -58400.5, 110337, 0, 0
2015-07-03T16:46:10:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T16:46:10:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T16:46:11: 
2015-07-03T16:46:11: +=========================================+
2015-07-03T16:46:11: | Maximum likelihood optimization results |
2015-07-03T16:46:11: +=========================================+
2015-07-03T16:46:11: === GOptimizerLM ===
2015-07-03T16:46:11:  Optimized function value ..: 14851.928
2015-07-03T16:46:11:  Absolute precision ........: 0.005
2015-07-03T16:46:11:  Acceptable value decrease .: 2
2015-07-03T16:46:11:  Optimization status .......: converged
2015-07-03T16:46:11:  Number of parameters ......: 10
2015-07-03T16:46:11:  Number of free parameters .: 4
2015-07-03T16:46:11:  Number of iterations ......: 2
2015-07-03T16:46:11:  Lambda ....................: 1e-05
2015-07-03T16:46:11:  Maximum log likelihood ....: -14851.928
2015-07-03T16:46:11:  Observed events  (Nobs) ...: 45144.000
2015-07-03T16:46:11:  Predicted events (Npred) ..: 45143.998 (Nobs - Npred = 0.0015177)

#11 Updated by Knödlseder Jürgen over 7 years ago

I checked the difference between a model map computed from the IRFs and a model map computed from the cube response, for the same input parameters and observation definition (1800 seconds, Crab as a single source).

I used the following script to compute the residual map:

import gammalib

map_irf     = gammalib.GSkyMap("modcube_irf.fits")
map_stacked = gammalib.GSkyMap("modcube_stacked.fits")

residual = (map_irf - map_stacked) / map_irf

residual.save("residual.fits", True)

There is a ring-like residual at the position of the Crab, but the amplitude of this residual in individual pixels does not exceed 1-2%. Attached the generated FITS file (residual.fits.gz). The response computation is thus consistent.

#12 Updated by Knödlseder Jürgen over 7 years ago

  • % Done changed from 10 to 50

I finally found the bug in the Npred computation: when removing the deadtime correction I also removed some renormalization of the gradients that was needed to get their right amplitude. The gradients of the background model were thus wrong. This is now corrected.

For reference, here the fit when using the IRF computation for the binned analysis:

2015-07-03T21:32:26: +=================================+
2015-07-03T21:32:26: | Maximum likelihood optimisation |
2015-07-03T21:32:26: +=================================+
2015-07-03T21:32:28:  >Iteration   0: -logL=39901.606, Lambda=1.0e-03
2015-07-03T21:32:29:  >Iteration   1: -logL=39899.679, Lambda=1.0e-03, delta=1.928, max(|grad|)=6.256420 [Index:7]
2015-07-03T21:32:31:  >Iteration   2: -logL=39899.678, Lambda=1.0e-04, delta=0.001, max(|grad|)=-0.059539 [Index:3]
2015-07-03T21:32:31:  
2015-07-03T21:32:31:  +==================+
2015-07-03T21:32:31:  | Curvature matrix |
2015-07-03T21:32:31:  +==================+
2015-07-03T21:32:31:  === GMatrixSparse ===
2015-07-03T21:32:31:   Number of rows ............: 10
2015-07-03T21:32:31:   Number of columns .........: 10
2015-07-03T21:32:31:   Number of nonzero elements : 16
2015-07-03T21:32:31:   Number of allocated cells .: 528
2015-07-03T21:32:31:   Memory block size .........: 512
2015-07-03T21:32:31:   Sparse matrix fill ........: 0.16
2015-07-03T21:32:31:   Pending element ...........: 0
2015-07-03T21:32:31:   Fill stack size ...........: 0 (none)
2015-07-03T21:32:31:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T21:32:31:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T21:32:31:   0, 0, 83.7417, -95.0523, 0, 0, 25.4407, -46.9068, 0, 0
2015-07-03T21:32:31:   0, 0, -95.0523, 3812.11, 0, 0, 89.0835, -199.93, 0, 0
2015-07-03T21:32:31:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T21:32:31:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T21:32:31:   0, 0, 25.4407, 89.0835, 0, 0, 9879.25, -16499.1, 0, 0
2015-07-03T21:32:31:   0, 0, -46.9068, -199.93, 0, 0, -16499.1, 31620.7, 0, 0
2015-07-03T21:32:31:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T21:32:31:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T21:32:32: 
2015-07-03T21:32:32: +=========================================+
2015-07-03T21:32:32: | Maximum likelihood optimization results |
2015-07-03T21:32:32: +=========================================+
2015-07-03T21:32:32: === GOptimizerLM ===
2015-07-03T21:32:32:  Optimized function value ..: 39899.678
2015-07-03T21:32:32:  Absolute precision ........: 0.005
2015-07-03T21:32:32:  Acceptable value decrease .: 2
2015-07-03T21:32:32:  Optimization status .......: converged
2015-07-03T21:32:32:  Number of parameters ......: 10
2015-07-03T21:32:32:  Number of free parameters .: 4
2015-07-03T21:32:32:  Number of iterations ......: 2
2015-07-03T21:32:32:  Lambda ....................: 1e-05
2015-07-03T21:32:32:  Maximum log likelihood ....: -39899.678
2015-07-03T21:32:32:  Observed events  (Nobs) ...: 13359.000
2015-07-03T21:32:32:  Predicted events (Npred) ..: 13358.998 (Nobs - Npred = 0.00151521)
2015-07-03T21:32:32: === GModels ===
2015-07-03T21:32:32:  Number of models ..........: 2
2015-07-03T21:32:32:  Number of parameters ......: 10
2015-07-03T21:32:32: === GModelSky ===
2015-07-03T21:32:32:  Name ......................: Crab
2015-07-03T21:32:32:  Instruments ...............: all
2015-07-03T21:32:32:  Instrument scale factors ..: unity
2015-07-03T21:32:32:  Observation identifiers ...: all
2015-07-03T21:32:32:  Model type ................: PointSource
2015-07-03T21:32:32:  Model components ..........: "SkyDirFunction" * "PowerLaw" * "Constant" 
2015-07-03T21:32:32:  Number of parameters ......: 6
2015-07-03T21:32:32:  Number of spatial par's ...: 2
2015-07-03T21:32:32:   RA .......................: 83.6331 [-360,360] deg (fixed,scale=1)
2015-07-03T21:32:32:   DEC ......................: 22.0145 [-90,90] deg (fixed,scale=1)
2015-07-03T21:32:32:  Number of spectral par's ..: 3
2015-07-03T21:32:32:   Prefactor ................: 5.78359e-16 +/- 1.10915e-17 [1e-23,1e-13] ph/cm2/s/MeV (free,scale=1e-16,gradient)
2015-07-03T21:32:32:   Index ....................: -2.49196 +/- 0.0164354 [-0,-5]  (free,scale=-1,gradient)
2015-07-03T21:32:32:   PivotEnergy ..............: 300000 [10000,1e+09] MeV (fixed,scale=1e+06,gradient)
2015-07-03T21:32:32:  Number of temporal par's ..: 1
2015-07-03T21:32:32:   Normalization ............: 1 (relative value) (fixed,scale=1,gradient)
2015-07-03T21:32:32: === GCTAModelIrfBackground ===
2015-07-03T21:32:32:  Name ......................: CTABackgroundModel
2015-07-03T21:32:32:  Instruments ...............: CTA
2015-07-03T21:32:32:  Instrument scale factors ..: unity
2015-07-03T21:32:32:  Observation identifiers ...: all
2015-07-03T21:32:32:  Model type ................: "PowerLaw" * "Constant" 
2015-07-03T21:32:32:  Number of parameters ......: 4
2015-07-03T21:32:32:  Number of spectral par's ..: 3
2015-07-03T21:32:32:   Prefactor ................: 1.01899 +/- 0.0280579 [0.001,1000] ph/cm2/s/MeV (free,scale=1,gradient)
2015-07-03T21:32:32:   Index ....................: 0.0189749 +/- 0.0156848 [-5,5]  (free,scale=1,gradient)
2015-07-03T21:32:32:   PivotEnergy ..............: 1e+06 [10000,1e+09] MeV (fixed,scale=1e+06,gradient)
2015-07-03T21:32:32:  Number of temporal par's ..: 1
2015-07-03T21:32:32:   Normalization ............: 1 (relative value) (fixed,scale=1,gradient)

And here the same for the stacked analysis (now is basically identical):

2015-07-03T21:48:48: +=================================+
2015-07-03T21:48:48: | Maximum likelihood optimisation |
2015-07-03T21:48:48: +=================================+
2015-07-03T21:48:49:  >Iteration   0: -logL=39901.545, Lambda=1.0e-03
2015-07-03T21:48:50:  >Iteration   1: -logL=39899.629, Lambda=1.0e-03, delta=1.916, max(|grad|)=6.221122 [Index:7]
2015-07-03T21:48:51:  >Iteration   2: -logL=39899.628, Lambda=1.0e-04, delta=0.001, max(|grad|)=-0.060144 [Index:3]
2015-07-03T21:48:51:  
2015-07-03T21:48:51:  +==================+
2015-07-03T21:48:51:  | Curvature matrix |
2015-07-03T21:48:51:  +==================+
2015-07-03T21:48:51:  === GMatrixSparse ===
2015-07-03T21:48:51:   Number of rows ............: 10
2015-07-03T21:48:51:   Number of columns .........: 10
2015-07-03T21:48:51:   Number of nonzero elements : 16
2015-07-03T21:48:51:   Number of allocated cells .: 528
2015-07-03T21:48:51:   Memory block size .........: 512
2015-07-03T21:48:51:   Sparse matrix fill ........: 0.16
2015-07-03T21:48:51:   Pending element ...........: 0
2015-07-03T21:48:51:   Fill stack size ...........: 0 (none)
2015-07-03T21:48:51:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T21:48:51:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T21:48:51:   0, 0, 83.7761, -95.0742, 0, 0, 25.3675, -46.7484, 0, 0
2015-07-03T21:48:51:   0, 0, -95.0742, 3812.14, 0, 0, 88.6885, -199.063, 0, 0
2015-07-03T21:48:51:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T21:48:51:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T21:48:51:   0, 0, 25.3675, 88.6885, 0, 0, 9881.05, -16501.8, 0, 0
2015-07-03T21:48:51:   0, 0, -46.7484, -199.063, 0, 0, -16501.8, 31624.7, 0, 0
2015-07-03T21:48:51:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T21:48:51:   0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2015-07-03T21:48:52: 
2015-07-03T21:48:52: +=========================================+
2015-07-03T21:48:52: | Maximum likelihood optimization results |
2015-07-03T21:48:52: +=========================================+
2015-07-03T21:48:52: === GOptimizerLM ===
2015-07-03T21:48:52:  Optimized function value ..: 39899.628
2015-07-03T21:48:52:  Absolute precision ........: 0.005
2015-07-03T21:48:52:  Acceptable value decrease .: 2
2015-07-03T21:48:52:  Optimization status .......: converged
2015-07-03T21:48:52:  Number of parameters ......: 10
2015-07-03T21:48:52:  Number of free parameters .: 4
2015-07-03T21:48:52:  Number of iterations ......: 2
2015-07-03T21:48:52:  Lambda ....................: 1e-05
2015-07-03T21:48:52:  Maximum log likelihood ....: -39899.628
2015-07-03T21:48:52:  Observed events  (Nobs) ...: 13359.000
2015-07-03T21:48:52:  Predicted events (Npred) ..: 13358.998 (Nobs - Npred = 0.00150876)
2015-07-03T21:48:52: === GModels ===
2015-07-03T21:48:52:  Number of models ..........: 2
2015-07-03T21:48:52:  Number of parameters ......: 10
2015-07-03T21:48:52: === GModelSky ===
2015-07-03T21:48:52:  Name ......................: Crab
2015-07-03T21:48:52:  Instruments ...............: all
2015-07-03T21:48:52:  Instrument scale factors ..: unity
2015-07-03T21:48:52:  Observation identifiers ...: all
2015-07-03T21:48:52:  Model type ................: PointSource
2015-07-03T21:48:52:  Model components ..........: "SkyDirFunction" * "PowerLaw" * "Constant" 
2015-07-03T21:48:52:  Number of parameters ......: 6
2015-07-03T21:48:52:  Number of spatial par's ...: 2
2015-07-03T21:48:52:   RA .......................: 83.6331 [-360,360] deg (fixed,scale=1)
2015-07-03T21:48:52:   DEC ......................: 22.0145 [-90,90] deg (fixed,scale=1)
2015-07-03T21:48:52:  Number of spectral par's ..: 3
2015-07-03T21:48:52:   Prefactor ................: 5.78242e-16 +/- 1.10892e-17 [1e-23,1e-13] ph/cm2/s/MeV (free,scale=1e-16,gradient)
2015-07-03T21:48:52:   Index ....................: -2.49208 +/- 0.0164353 [-0,-5]  (free,scale=-1,gradient)
2015-07-03T21:48:52:   PivotEnergy ..............: 300000 [10000,1e+09] MeV (fixed,scale=1e+06,gradient)
2015-07-03T21:48:52:  Number of temporal par's ..: 1
2015-07-03T21:48:52:   Normalization ............: 1 (relative value) (fixed,scale=1,gradient)
2015-07-03T21:48:52: === GCTAModelCubeBackground ===
2015-07-03T21:48:52:  Name ......................: BackgroundModel
2015-07-03T21:48:52:  Instruments ...............: CTA, HESS, MAGIC, VERITAS
2015-07-03T21:48:52:  Instrument scale factors ..: unity
2015-07-03T21:48:52:  Observation identifiers ...: all
2015-07-03T21:48:52:  Model type ................: "PowerLaw" * "Constant" 
2015-07-03T21:48:52:  Number of parameters ......: 4
2015-07-03T21:48:52:  Number of spectral par's ..: 3
2015-07-03T21:48:52:   Prefactor ................: 1.01894 +/- 0.0280565 [0,infty[ ph/cm2/s/MeV (free,scale=1,gradient)
2015-07-03T21:48:52:   Index ....................: 0.0189205 +/- 0.0156844 [-10,10]  (free,scale=1,gradient)
2015-07-03T21:48:52:   PivotEnergy ..............: 1e+06 MeV (fixed,scale=1e+06,gradient)
2015-07-03T21:48:52:  Number of temporal par's ..: 1
2015-07-03T21:48:52:   Normalization ............: 1 (relative value) (fixed,scale=1,gradient)

What remains to be understood is why the pull distribution of the classical binned and the stacked analyses have a bias when using a large field.

#13 Updated by Knödlseder Jürgen over 7 years ago

  • % Done changed from 50 to 90

I understand the problem!

A bias occurs if the binning used is not sufficiently fine grained. In the actual simulations, a binning of 0.05 deg / pixel was used. This is slightly worse than the best angular resolution and introduces a biases, in particular in the fitted spectral index.

Here for reference the results for a 0.05 deg / pixel spatial binning:
And here the results for a 0.02 deg / pixel spatial binning (same area covered, hence the number of spatial pixels was 250 x 250 instead of 100 x 100 before):

#16 Updated by Knödlseder Jürgen over 7 years ago

  • Status changed from In Progress to Feedback
  • % Done changed from 90 to 100

I put this issue now on feedback.

We still need to do more pull distributions. I plan to do one for all spectral laws so that we also have a reference for the stacked analysis.

#17 Updated by Knödlseder Jürgen over 7 years ago

Here some more results for 0.02° spatial binning an 10, 15, 20, 30 and 40 energy bins between 0.1 and 100 TeV. At least 30 energy bins are needed to reduce the bias to an acceptable level.

#18 Updated by Knödlseder Jürgen about 7 years ago

  • Status changed from Feedback to Closed

Close this now as the issue was related to a limited number of bins in the initial runs that suggested a problem.

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