Difference between revisions of "LFI-Validation"

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{{DISPLAYTITLE:Internal overall validation}}
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{{DISPLAYTITLE:Overall internal validation}}
 
== Overview ==
 
== Overview ==
Data validation is critical at each step of the analysis pipeline.  Much of the LFI data validation is based on null tests. Here we present some examples from the current release, with comments on relevant time scales and sensitivity to various systematics.
+
Data validation is critical at each step of the analysis pipeline.  Much of the LFI data validation is based on null tests. Here we present some examples from the current release, with comments on relevant time scales and sensitivity to various systematics. In the 2018 release in addition we perform many test to verify the differences between this and previous release (see {{PlanckPapers|planck2016-l02}}).
 +
 
 
== Null tests approach ==
 
== Null tests approach ==
Null tests at map level are performed routinely, whenever changes are made to the mapmaking pipeline.  These include differences at survey, year, 2 year, half mission and ringhalf levels, for single detectors, horns, horn pairs and full frequency complements.  Where possible, map differences are generated in I, Q and U.  
+
Null tests at map level are performed routinely, whenever changes are made to the mapmaking pipeline.  These include differences at survey, year, 2-year, half- mission and half-ring levels, for single detectors, horns, horn pairs and full frequency complements.  Where possible, map differences are generated in <i>I</i>, <i>Q</i> and <i>U</i>.  
For this release, we use the Full Focal Plane 8 (FFP8) simulations for comparison. We can use FFP8 noise simulations, identical to the data in terms of sky sampling and with matching time domain noise characteristics, to make statistical arguments about the likelihood of the noise observed in the actual data nulls.
+
For this release, we use the Full Focal Plane 10 (FFP10) simulations for comparison. We can use FFP10 noise simulations, identical to the data in terms of sky sampling and with matching time domain noise characteristics, to make statistical arguments about the likelihood of the noise observed in the actual data nulls.
In general null tests are performed in order to highlight possible issues in the data related to instrumental  systematic effecst not properly accounted for within the processing pipeline, or related to known changes in the operational conditions (e.g. switch-over of the sorption coolers), or related to intrinsic instrument properties coupled with the sky signal, such as stray light contamination.
+
In general null tests are performed to highlight possible issues in the data related to instrumental  systematic effecst not properly accounted for within the processing pipeline, or related to known changes in the operational conditions (e.g., switch-over of the sorption coolers), or related to intrinsic instrument properties coupled with the sky signal, such as stray light contamination.
Such null-tests can be performed using data on different time scales ranging from one minute to one year of observations, at different unit levels (radiometer, horn, horn-pair), within frequency and cross-frequency, both in total intensity, and, when applicable, in polarisation.
+
Such null-tests can be performed by using data on different time scales ranging from 1 minute to 1 year of observations, at different unit levels (radiometer, horn, horn-pair), within frequency and cross-frequency, both in total intensity, and, when applicable, in polarization.
 +
 
 
=== Sample Null Maps ===
 
=== Sample Null Maps ===
  
<gallery>
+
[[File:Fig_13.png|thumb|center|900px]]
File:PlanckFig_map_Diff030full_ringhalf_1-full_ringhalf_2sm3I_Stokes_88mm.png
 
File:PlanckFig_map_Diff030full_ringhalf_1-full_ringhalf_2sm3Q_Stokes_88mm.png
 
File:PlanckFig_map_Diff030yr1+yr3-yr2+yr4sm3Q_Stokes_88mm.png
 
File:PlanckFig_map_Diff030yr1+yr3-yr2+yr4sm3I_Stokes_88mm.png
 
</gallery>
 
<gallery>
 
File:PlanckFig_map_Diff044full_ringhalf_1-full_ringhalf_2sm3I_Stokes_88mm.png
 
File:PlanckFig_map_Diff044full_ringhalf_1-full_ringhalf_2sm3Q_Stokes_88mm.png
 
File:PlanckFig_map_Diff044yr1+yr3-yr2+yr4sm3Q_Stokes_88mm.png
 
File:PlanckFig_map_Diff044yr1+yr3-yr2+yr4sm3I_Stokes_88mm.png
 
</gallery>
 
<gallery>
 
File:PlanckFig_map_Diff070full_ringhalf_1-full_ringhalf_2sm3I_Stokes_88mm.png
 
File:PlanckFig_map_Diff070full_ringhalf_1-full_ringhalf_2sm3Q_Stokes_88mm.png
 
File:PlanckFig_map_Diff070yr1+yr3-yr2+yr4sm3Q_Stokes_88mm.png
 
File:PlanckFig_map_Diff070yr1+yr3-yr2+yr4sm3I_Stokes_88mm.png
 
</gallery>
 
'''Null map samples: top to bottom 30,44,70GHz; Left to right: ringhalf differences I, Q, 2 year combination differences I, Q. All maps smoothed to 3 degrees'''
 
  
 +
This figure shows difefrences between 2018 and 1015 frequenncy maps in <i>I</i>, <i>Q</i> and <i>U</i>. Large scale differences between the two set of maps are mainly due to changes in the calibration procedure.
  
 +
[[File:Fig_14.png|thumb|center|900px]]
  
Three things are worth pointing out generally about these maps.
+
In this figure we consider the set of odd-even survey differences combining all eight sky surveys covered by LFI. These survey combinations optimize the signal-to-noise ratio and highlight
First- there are no obvious 'features' standing out at this resolution and noise level. Earlier versions of the data processing, where there were errors in calibration for instance, would show scan-correlated structures at much larger amplitude.
+
large-scale structures. The nine maps on the left show odd-even survey dfferences for the 2015 release, while the nine maps on the right show the same for the 2018 release. The 2015 data show large residuals in <i>I</i> at 30 and 44 GHz that bias the difference away from zero. This effect is considerably reduced in the 2018 release, as expected from the improvements in the calibration process. The <i>I</i> map at 70 GHz also shows a significant improvement. In the polarization maps, there is a general reduction in the amplitude of structures close to the Galactic plane.
Second- The half-ring difference maps and the2 year combination differnce maps give a very similar overall impression. This is a very good sign, as these two typese of null cover very different time scales (1 hour to 2 years).
 
Third- Its impossible to know how 'good' the test is just by looking at the map. There is clearly noise, but determining if it is consistent with the noise model of the instrument, and further, if it will bias the scientific results, requires more analsysis.
 
===Statistical Analyses===
 
The next level of data compression is to use the angular power spectra of the null tests, and to compare to simulations in a statistically robust way. We use two different approaches.
 
In the first we compare pseudospectra of the null maps to the half ring spectra, which are the most 'free' of anticipated systmatics.
 
In the second, we use noise monte carlos from the FFP8 simulations, where we run the mapmaking identically to the real data, over data sets with identical sampling to the real data but consisting of noise only generated to match the per-detector LFI noise model.  
 
  
Together with images, power spectra of the residual are also produced and compared with the expected level of white noise
+
[[File:Fig_15.png|thumb|center|400px]]
derived from the half-ring jack-knifes. With these quantities are combined to produce a sort of <math>\chi^2</math>. This gives an indication of the deviation of the residuals with respect to the white noise level. Of course underlying signal does not posses a Gaussian statistic and therefore with non-Gaussian data, the <math>\chi^2</math> tests is less meaningful. However this gives an hint on the presence of residuals which in some cases are indeed expected: in fact making difference between odd and even survey at horn and frequency level, is a way to show the signature of the external stray-light which, although properly accounted for during the calibration procedure, has not been removed from the data.
 
  
 +
Finally here we shows pseudo-angular power spectra from the oddeven survey dfferences. There is great improvement in 2018 in removing largescale structures at 30 GHz in <i>TT</i>, <i>EE</i>, and somewhat in <i>BB</i>, and also in <i>TT</i> at 44 GHz.
  
Here we show examples comparing the pseudospectra of a set of 100 monte carlos to the real data. We mask both data and simlations to concentrate on residuals impactin CMB analyses away from the galactic plane.
 
(I'll include some plots of error bars from FFP8 per ell overlaid with data nulls (maybe same nulls as above)
 
Finally, we can look at the distribution of noise power from the monte carlos 'ell by ell' and check where the real data fall in that distribution, to see if it is consistent with noise alone.
 
(here I'll put some of the histogram comparisons for the low ell as seen in the DPC paper)
 
==Consistency checks ==
 
  
All the details can be found in {{PlanckPapers|planck2013-p02}} {{PlanckPapers|planck2014-a03||Planck-2015-A03}}.  
+
===Intra-frequency consistency check===
 +
We have tested the consistency between 30, 44, and 70GHz maps by comparing the power spectra in the multipole range around the first acoustic peak. In order to do so, we have removed the estimated contribution from unresolved point source from the spectra. We have then built scatter plots for the three frequency pairs, i.e., 70GHz versus 30 GHz, 70GHz versus 44GHz, and 44GHz versus 30GHz, and performed a linear fit, accounting for errors on both axes.
 +
The results reported below show that the three power spectra are consistent within the errors. Moreover, note that the current error budget does not account for foreground removal, calibration, and window function uncertainties. Hence, the observed agreement between spectra at different frequencies can be considered to be even more satisfactory.
  
===Intra frequency consistency check===
+
[[File:Fig_21.png|thumb|center|1200px]]
We have tested the consistency between 30, 44, and 70 GHz maps by comparing the power spectra in the multipole range around the first acoustic peak. In order to do so, we have removed the estimated contribution from unresolved point source from the spectra. We have then built the scatter plots for the three frequency pairs, i.e. 70 vs 30 GHz, 70 vs 44 GHz, and 44 vs 30 GHz, and performed a linear fit accounting for errors on both axis.
 
The results reported in Fig. 1 show that the three power spectra are consistent within the errors. Moreover, please note that current error budget does not account for foreground removal, calibration, and window function uncertainties. Hence, the resulting agreement between spectra at different frequencies can be fairly considered even more significant.
 
  
[[File:LFI_70vs44_DX11D_maskTCS070vs060_a.jpg|thumb|center|400px|]][[File:LFI_70vs30_DX11D_maskTCS070vs040_a.jpg|thumb|center|400px|]][[File:LFI_44vs30_DX11D_maskTCS060vs040_a.jpg|thumb|center|400px|'''Figure 1. Consistency between spectral estimates at different frequencies. From top to bottom: 70 vs 44 GHz; 70 vs 30 GHz; 44 vs 30 GHz. Solid red lines are the best fit of the linear regressions, whose angular coefficients <math>\alpha</math> are consistent with 1 within the errors.''']]
 
  
 
===70 GHz internal consistency check===
 
===70 GHz internal consistency check===
We use the Hausman test {{BibCite|polenta_CrossSpectra}} to assess the consistency of auto and cross spectral estimates at 70 GHz. We define the statistic:
+
We use the Hausman test {{BibCite|polenta_CrossSpectra}} to assess the consistency of auto- and cross-spectral estimates at 70 GHz. We specifically define the statistic:
  
 
:<math>
 
:<math>
H_{\ell}=\left(\hat{C_{\ell}}-\tilde{C_{\ell}}\right)/\sqrt{Var\left\{ \hat{C_{\ell}}-\tilde{C_{\ell}}\right\} }
+
H_{\ell}=\left(\hat{C_{\ell}}-\tilde{C_{\ell}}\right)/\sqrt{{\rm Var}\left\{ \hat{C_{\ell}}-\tilde{C_{\ell}}\right\} },
 
</math>
 
</math>
  
where <math>\hat{C_{\ell}}</math> and <math>\tilde{C_{\ell}}</math> represent auto- and
+
where <math>\hat{C_{\ell}}</math> and <math>\tilde{C_{\ell}}</math> represent auto- and
cross-spectra respectively. In order to combine information from different multipoles into a single quantity, we define the following quantity:
+
cross-spectra, respectively. In order to combine information from different multipoles into a single quantity, we define
  
 
:<math>
 
:<math>
B_{L}(r)=\frac{1}{\sqrt{L}}\sum_{\ell=2}^{[Lr]}H_{\ell},r\in\left[0,1\right]
+
B_{L}(r)=\frac{1}{\sqrt{L}}\sum_{\ell=2}^{[Lr]}H_{\ell},r\in\left[0,1\right],
 
</math>
 
</math>
  
where <math>[.]</math> denotes integer part. The distribution of <math>B_{L}(r)</math>
+
where square brackets denote the integer part. The distribution of <i>B<sub>L</sub></i>(<i>r</i>)
 
converges (in a functional sense) to a Brownian motion process, which can be studied through the statistics
 
converges (in a functional sense) to a Brownian motion process, which can be studied through the statistics
<math>s_{1}=\textrm{sup}_{r}B_{L}(r)</math>
+
<i>s</i><sub>1</sub>=sup<sub><i>r</i></sub><i>B<sub>L</sub></i>(<i>r</i>),
<math>s_{2}=\textrm{sup}_{r}|B_{L}(r)|</math> and
+
<i>s</i><sub>2</sub>=sup<sub><i>r</i></sub>|<i>B<sub>L</sub></i>(<i>r</i>)|, and
<math>s_{3}=\int_{0}^{1}B_{L}^{2}(r)dr</math>. Using the ''FFP7'' simulations
+
<i>s</i><sub>3</sub>=&#8747;<sub>0</sub><sup>1</sup><i>B<sub>L</sub></i><sup>2</sup>(<i>r</i>)dr. Using the "FFP10" simulations,
we derive the empirical distribution for all the three test statistics and we compare with results obtained from Planck data
+
we derive empirical distributions for all the three test statistics and compare with results obtained from Planck data. We find that the Hausman test shows no statistically significant inconsistencies between the two spectral
(see Fig. 2). Thus, the Hausman test shows no statistically significant inconsistencies between the two spectral
 
 
estimates.
 
estimates.
  
[[File:cons2.jpg|thumb|center|800px|'''Figure 2. From left to right, the empirical
+
[[File:Fig_23.png|thumb|center|1200px|]]
distribution (estimated via ''FFP7'') of the <math>s_{1},s_{2},s_{3}</math>
 
statistics (see text). The vertical line represents 70 GHz data.''']]
 
 
 
As a further test, we have estimated the temperature power spectrum for each of three horn-pair map, and we have compared the
 
results with the spectrum obtained from all the 12 radiometers shown above. In Fig. 3 we show the
 
difference between the horn-pair and the combined power spectra.
 
Again, the error bars have been estimated from the ''FFP7'' simulated dataset. A <math>\chi^{2}</math> analysis of the residual shows that they are compatible with the null hypothesis, confirming the
 
strong consistency of the estimates.
 
 
 
[[File:cons3.jpg|thumb|center|500px|'''Figure 3. Residuals between the auto power spectra of the horn pair maps and the power spectrum of the full 70 GHz frequency map. Error bars are derived from ''FFP7'' simulations.''']]
 
  
 
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Latest revision as of 11:09, 6 July 2018

Overview[edit]

Data validation is critical at each step of the analysis pipeline. Much of the LFI data validation is based on null tests. Here we present some examples from the current release, with comments on relevant time scales and sensitivity to various systematics. In the 2018 release in addition we perform many test to verify the differences between this and previous release (see Planck-2020-A2[1]).

Null tests approach[edit]

Null tests at map level are performed routinely, whenever changes are made to the mapmaking pipeline. These include differences at survey, year, 2-year, half- mission and half-ring levels, for single detectors, horns, horn pairs and full frequency complements. Where possible, map differences are generated in I, Q and U. For this release, we use the Full Focal Plane 10 (FFP10) simulations for comparison. We can use FFP10 noise simulations, identical to the data in terms of sky sampling and with matching time domain noise characteristics, to make statistical arguments about the likelihood of the noise observed in the actual data nulls. In general null tests are performed to highlight possible issues in the data related to instrumental systematic effecst not properly accounted for within the processing pipeline, or related to known changes in the operational conditions (e.g., switch-over of the sorption coolers), or related to intrinsic instrument properties coupled with the sky signal, such as stray light contamination. Such null-tests can be performed by using data on different time scales ranging from 1 minute to 1 year of observations, at different unit levels (radiometer, horn, horn-pair), within frequency and cross-frequency, both in total intensity, and, when applicable, in polarization.

Sample Null Maps[edit]

Fig 13.png

This figure shows difefrences between 2018 and 1015 frequenncy maps in I, Q and U. Large scale differences between the two set of maps are mainly due to changes in the calibration procedure.

Fig 14.png

In this figure we consider the set of odd-even survey differences combining all eight sky surveys covered by LFI. These survey combinations optimize the signal-to-noise ratio and highlight large-scale structures. The nine maps on the left show odd-even survey dfferences for the 2015 release, while the nine maps on the right show the same for the 2018 release. The 2015 data show large residuals in I at 30 and 44 GHz that bias the difference away from zero. This effect is considerably reduced in the 2018 release, as expected from the improvements in the calibration process. The I map at 70 GHz also shows a significant improvement. In the polarization maps, there is a general reduction in the amplitude of structures close to the Galactic plane.

Fig 15.png

Finally here we shows pseudo-angular power spectra from the oddeven survey dfferences. There is great improvement in 2018 in removing largescale structures at 30 GHz in TT, EE, and somewhat in BB, and also in TT at 44 GHz.


Intra-frequency consistency check[edit]

We have tested the consistency between 30, 44, and 70GHz maps by comparing the power spectra in the multipole range around the first acoustic peak. In order to do so, we have removed the estimated contribution from unresolved point source from the spectra. We have then built scatter plots for the three frequency pairs, i.e., 70GHz versus 30 GHz, 70GHz versus 44GHz, and 44GHz versus 30GHz, and performed a linear fit, accounting for errors on both axes. The results reported below show that the three power spectra are consistent within the errors. Moreover, note that the current error budget does not account for foreground removal, calibration, and window function uncertainties. Hence, the observed agreement between spectra at different frequencies can be considered to be even more satisfactory.

Fig 21.png


70 GHz internal consistency check[edit]

We use the Hausman test [2] to assess the consistency of auto- and cross-spectral estimates at 70 GHz. We specifically define the statistic:

[math] H_{\ell}=\left(\hat{C_{\ell}}-\tilde{C_{\ell}}\right)/\sqrt{{\rm Var}\left\{ \hat{C_{\ell}}-\tilde{C_{\ell}}\right\} }, [/math]

where [math]\hat{C_{\ell}}[/math] and [math]\tilde{C_{\ell}}[/math] represent auto- and cross-spectra, respectively. In order to combine information from different multipoles into a single quantity, we define

[math] B_{L}(r)=\frac{1}{\sqrt{L}}\sum_{\ell=2}^{[Lr]}H_{\ell},r\in\left[0,1\right], [/math]

where square brackets denote the integer part. The distribution of BL(r) converges (in a functional sense) to a Brownian motion process, which can be studied through the statistics s1=suprBL(r), s2=supr|BL(r)|, and s3=∫01BL2(r)dr. Using the "FFP10" simulations, we derive empirical distributions for all the three test statistics and compare with results obtained from Planck data. We find that the Hausman test shows no statistically significant inconsistencies between the two spectral estimates.

Fig 23.png


References[edit]

  1. Planck 2018 results. II. Low Frequency Instrument data processing, Planck Collaboration, 2020, A&A, 641, A2.
  2. Unbiased estimation of an angular power spectrum, G. Polenta, D. Marinucci, A. Balbi, P. de Bernardis, E. Hivon, S. Masi, P. Natoli, N. Vittorio, J. Cosmology Astropart. Phys., 11, 1, (2005).

(Planck) Low Frequency Instrument