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  1. 1. MLE spectrum tests :
    1. 1.1 Pre-tests :
  2. 2. Comparison MLE and my code :
    1. 2.1 ds_dcb Matrix Pl :
    2. 2.2 Signal Matrix S :

1.  MLE spectrum tests :

1.1  Pre-tests :

  • Full vs fsky=0.5.
  • 300 simus.
 EstimatorVariance
1.0 muK
0.001 muK
  • Big problem of biais and error ...

2.  Comparison MLE and my code :

2.1  ds_dcb Matrix Pl :

Comparison between \frac {d S}{d C_\ell} (mine, and 'JC' MLE python code), QU-polar, nside=2 (same kind of result for temperature). Matrices are flattenenned then plotted :

  • on each plots : first half is EE, second half is BB. The difference between 0 to 20000 is due to a different calculation of ds_dcb for the two first \ell =0,1 , but has no effect later, since C_0^{th} = C_1^{th} = 0
  • The left plot highlight a difference for the last \ell in both EE and BB. This si due to a error in the MLE code : the last bin is put to 3*nside instead of 3*nside-1. If corrected, we (almost) recover the same aspect for the last bin (right plot)
  • Other small differences are present, and come from error in the MLE calculation. Those have indeed implication in the Signal Matrix S computation :

2.2  Signal Matrix S :

Comparison between Monte-carlo generated 'S' matrix and \displaystyle C_\ell \frac {d S}{d C_\ell} (mine, and 'JC' MLE python code). 1000 simulations for MC, QU-polar, nside=4 (same kind of result for temperature) Matrices are flattenenned then plotted :

  • My code recover correctly the MC covariance matrix.
  • We see that the error in the ds_dcb MLE matrix has impact for some pixels covariance in the S matrix calculation.