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  1. 1. effective fsky :
    1. 1.1 Bicep :
    2. 1.2 LiB :
  2. 2. Xpol VS Pure VS xQML :
    1. 2.1 Bicep :
    2. 2.2 LiB :
  3. 3. Looking for no bias and optimal variance (V2) :
    1. 3.1 LiteBIRD
    2. 3.2 BICEP
  4. 4. Looking for no bias and optimal variance (previous version V1) :
    1. 4.1 LiteBIRD
    2. 4.2 BICEP
Attach:PuXp_opti_FULL_Ns16_Nbins46_r0.001_fsky0.7_muKarcm50.0EE_Sapo0.0_res32.png ΔAttach:PuXp_opti_FULL_Ns16_Nbins46_r0.001_fsky0.7_muKarcm50.0BB_Sapo0.0_res32.png ΔAttach:PuXp_opti_FULL_Ns16_Nbins46_r0.001_fsky0.7_muKarcm50.0EB_Sapo0.0_res32.png Δ

1.  effective fsky :

1.1  Bicep :

apo = 0ffsky= 0.0159
apo = 0.5ffsky= 0.0153
apo = 1ffsky= 0.0147
apo = 2ffsky= 0.0134
apo = 3ffsky= 0.0122
apo = 4ffsky= 0.0111
apo = 5ffsky= 0.00999
apo = 6ffsky= 0.00897
apo = 7ffsky= 0.00801
apo = 8ffsky= 0.00713
apo = 9ffsky= 0.00637
apo = 10ffsky= 0.00575

1.2  LiB :

apo = 0ffsky= 0.7
apo = 0.5ffsky= 0.694
apo = 1ffsky= 0.688
apo = 2ffsky= 0.676
apo = 3ffsky= 0.664
apo = 4ffsky= 0.652
apo = 5ffsky= 0.641
apo = 6ffsky= 0.63
apo = 7ffsky= 0.619
apo = 8ffsky= 0.608
apo = 9ffsky= 0.597
apo = 10ffsky= 0.587
apo = 15ffsky= 0.536
apo = 20ffsky= 0.489
apo = 25ffsky= 0.445
apo = 30ffsky= 0.404

2.  Xpol VS Pure VS xQML :

2.1  Bicep :

Sapo = 0.0
Sapo = 0.1
  • Comment :
    • erreur pour Xpol pour Sapo=0.1, beam mal corrigé (d'ou variance < xQML)

2.2  LiB :

Sapo = 0.0
Sapo = 1.0
Sapo = 2.0
Sapo = 3.0

3.  Looking for no bias and optimal variance (V2) :

  • Estimator results are plotted using the triangular markers
  • Corresponding estimator errors are plotted in dashed lines.
  • three types of mask smoothing : C!, C2, and Smooth
  1. In order to avoid any bias at low ell, the mask is pre-smoother using the Smooth apodisation at nside=512. The corresponding parameter is labeled "Sapo" for Smooth pre-apodisation (in degree)
  2. The pre-apodised mask is then smoothed using the C2 function parametrised by a apodisation lenght. The corresponding parameter is labeled "apo" (in degree)
  3. The apodised mask is then degraded to one nside above the xqml nside (ns=32 for LiB and ns=256 for BICEP).
  4. Pure estimator using NaMaster is then applied.

3.1  LiteBIRD

  • nside simu = 32
Sapo0.01.02.03.04.05.0
 Attach:Pure_FULL_Ns16_Nbins46_Slmaxmul3_fwhmdeg0.5_r0.001_fsky0.7_muKarcm0.1BB_Sapo0.0_res32.png Δ
  • nside simu = 128
Sapo0.01.02.03.04.05.0
 Attach:Pure_FULL_Ns16_Nbins46_Slmaxmul3_fwhmdeg0.5_r0.001_fsky0.7_muKarcm0.1BB_Sapo0.0_res128.png Δ

3.2  BICEP

  • nside simu = 256
  • 27 bins equaly distributed (delta ell = 14)
Sapo0.00.10.20.30.40.50.6
  • observations :
    • both xqml and pure spectrum errors are close to mode counting at high multipole.

Groupe first bins :

  • nside simu = 256
  • first bins going from ell=2 to ell=48 + 25 bins equally distributed (delta ell = 14)
Sapo0.00.1
binary mask apodised
Bicep public mask apodised 
  • observations :
    • spectrum is biased for too low apodisation (apo = 1.0)
    • public mask bicep increases cosmic variance at high ell.

4.  Looking for no bias and optimal variance (previous version V1) :

  • Estimator results are plotted using the triangular markers
  • Corresponding estimator errors are plotted in dashed lines.
  • three types of mask smoothing : C!, C2, and Smooth
  1. In order to avoid any bias at low ell, the mask is pre-smoother using the Smooth apodisation at nside=512. The corresponding parameter is labeled "Sapo" for Smooth pre-apodisation (in degree)
  2. The pre-apodised mask is then smoothed using the C2 function parametrised by a apodisation lenght. The corresponding parameter is labeled "apo" (in degree)
  3. The apodised mask is then degraded to one nside above the xqml nside (ns=32 for LiB and ns=256 for BICEP).
  4. Pure estimator using NaMaster is then applied.

4.1  LiteBIRD

Sapo1.02.03.04.05.0
 

4.2  BICEP

Group first bins :

Binary mask->paodisedBicep public pre-apodised mask ->apodised

New results :

previous results :

Sapo0.20.30.40.50.6