1.  Surveys reuslts bias test :

1.1  LiB :

• Residual computed from {$ R = (\hat C_\ell - C_\ell^{th}) / std(\hat C_\ell) \cdot \sqrt{n_{MC}} = (\hat C_\ell - C_\ell^{th}) / std(\langle \hat C_\ell \rangle )$}

LiB	BICEP

• with naked eye, we already see that LiB seems unbiased, while Bicep is biais mainly for the EE spectrum.

1.2  Biais ?

• Computing the number of point at 1, 2 or 3 sigma, that is to say {$ (|R|< \sigma)/n_{bins} $} with {$ \sigma = 1, 2, 3 $} : expecting the 68-95-99.7 rule.
• 100000 simulations

LiB :

	noise	1 sigma	2 sigma	3 sigma
R (EE)	0.10 muK	1s 0.804	2s 0.978	3s 1.000
R (EE)	1.00 muK	1s 0.826	2s 0.978	3s 1.000
R (EE)	10.00 muK	1s 0.804	2s 0.978	3s 1.000
R (BB)	0.10 muK	1s 0.848	2s 0.978	3s 1.000
R (BB)	1.00 muK	1s 0.783	2s 0.978	3s 1.000
R (BB)	10.00 muK	1s 0.783	2s 1.000	3s 1.000

• conclusion : No bias found. The 68-95-99.7 rule is pretty well verified.

BICEP :

R (EE)	0.10 muK	1s 0.556	2s 0.556	3s 0.593
R (EE)	1.00 muK	1s 0.556	2s 0.556	3s 0.556
R (EE)	10.00 muK	1s 0.556	2s 0.556	3s 0.593
R (BB)	0.10 muK	1s 0.815	2s 0.852	3s 0.889
R (BB)	1.00 muK	1s 0.815	2s 0.852	3s 0.889
R (BB)	10.00 muK	1s 0.852	2s 0.926	3s 0.926

• conclusion : bias found fo EE. This si due to the theoretical binned spectrum approximation {$ C_b = P_{b \ell} \cdot C_\ell $} and the fact that the EE spectrum is not flat enought.
• conclusion : less bias found fo BB. This si due to the theoretical binned spectrum approximation {$ C_b = P_{b \ell} \cdot C_\ell $}, but the BB spectrum is sufficiently flat.
• mode per mode :

	Bins number	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26
	Bins val	8.5	22.5	36.5	50.5	64.5	78.5	92.5	106.5	120.5	134.5	148.5	162.5	176.5	190.5	204.5	218.5	232.5	246.5	260.5	274.5	288.5	302.5	316.5	330.5	344.5	358.5	372.5
R (EE)	0.10 muK	9967.8	79.9	-11.0	-0.8	-7.1	-8.2	-7.6	-6.5	-6.4	-4.3	0.1	3.3	14.6	25.3	32.5	32.6	27.1	15.5	9.3	3.0	-1.2	-5.0	-7.9	-7.9	-24.6	41.8	-511.8
R (EE)	1.00 muK	9822.4	79.8	-11.2	-0.9	-6.8	-8.2	-7.5	-6.2	-6.4	-4.0	0.1	3.3	14.5	25.2	31.9	32.3	26.7	15.5	9.5	3.6	-0.7	-3.8	-6.8	-5.6	-26.9	66.5	-575.9
R (EE)	10.00 muK	7827.6	76.8	-12.2	-0.6	-5.8	-7.5	-7.1	-5.5	-5.6	-3.5	0.0	2.7	12.6	20.6	25.3	26.6	20.9	13.7	8.2	3.8	-0.9	-2.0	-4.7	-2.2	-24.7	71.8	-407.8
R (BB)	0.10 muK	37.8	3.9	-2.3	-0.3	0.5	0.6	0.1	2.1	-0.2	-1.1	1.8	0.0	-1.5	-2.1	-0.0	-2.0	-0.9	-3.2	-2.3	-3.3	-3.8	-6.2	-8.4	-2.9	-33.1	91.4	-585.5
R (BB)	1.00 muK	31.1	4.8	-2.7	-0.1	0.5	0.9	-0.3	2.3	0.1	-1.1	1.9	0.3	-1.3	-1.7	0.4	-2.7	0.6	-3.6	-1.2	-1.8	-2.7	-5.6	-4.6	-2.5	-23.0	41.7	-211.3
R (BB)	10.00 muK	-46.9	28.6	-10.3	3.5	-0.4	-0.1	0.4	1.3	0.5	0.2	-2.1	1.1	0.7	0.6	0.6	-1.8	-0.4	-0.9	0.5	0.0	-0.3	-3.8	-1.0	-2.6	-4.6	-1.7	-17.2

• first and last modes have to be neglected when computing a likelihood on 'r'.

2.  NaMaster dependence over r :

• namaster behaves badly when r-> 0 :
• Blue : ns=8
• Green : ns=16
• Red : ns=32
• dashed black : BB model
• y-label is wrong, it should be {$ C_\ell $}

r=0.1	r=0.01	r=0.001	r=0.0
input EE = TE = 0

• problem solved : mask aposisation incorrect.

3.  Pure Tests :

• LiB, _Ns16, Nbins46, Slmax=3, fwhmdeg0.5, r0.001, fsky0.7
• Color solid lines are the error of the spectrum std(Cl)
• Dashed black line is the spectrum model

0.1 muK
1.0 muK
5.0 muK
50.0 muK

4.  Estimation and Variance

• Leakage=False means ClEE =0

Survey	EE	BB
LiB, fsky=0.5
LiB, fsky=0.6
BIC, "fsky=0.0159"

5.  Vairance ratio :

	fsky=0.5	fsky=0.6
LiB EE
LiB BB