Table 00
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 484\) for model (04.00).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none-0.796±2.489-0.255±0.899-0.094±0.439-0.033±0.275
linear-0.783±2.560-0.208±1.008-0.046±0.567-0.011±0.406
Input \(r\) = 0.003
none2.126±2.6132.686±1.0812.874±0.6162.964±0.443
linear2.210±2.8002.784±1.2912.963±0.8083.015±0.608
Table 00b
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 146\) for model (04b.00).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none-0.736±1.704-0.147±0.8350.024±0.5770.090±0.486
linear-0.598±1.9170.007±1.066 0.117±0.8170.123±0.729
Input \(r\) = 0.003
none2.358±1.7502.912±0.9463.073±0.6713.139±0.561
linear2.454±2.0243.015±1.2133.125±0.9063.137±0.769
Table 00c
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 146\) for model (04c.00).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none-0.493±3.518-0.167±1.278-0.050±0.592-0.006±0.321
linear-0.564±3.619-0.182±1.409-0.036±0.7250.009±0.441
Input \(r\) = 0.003
none3.179±3.3053.007±1.3332.992±0.7102.996±0.485
linear3.165±3.4613.017±1.5893.016±0.9753.020±0.705
Table 01
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 500\) for model (04.01).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none0.225±2.5220.593±0.9310.590±0.4710.526±0.306
linear0.089±2.6380.494±1.1000.479±0.6380.387±0.445
Input \(r\) = 0.003
none3.139±2.6093.524±1.0943.569±0.6483.563±0.483
linear3.040±2.7683.469±1.2973.507±0.8453.462±0.654
Table 01b
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 150\) for model (04b.01).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none1.100±1.9081.527±0.9561.649±0.6721.703±0.571
linear0.990±2.0991.284±1.2051.240±0.9201.191±0.805
Input \(r\) = 0.003
none4.252±1.9084.626±1.0624.730±0.7784.777±0.667
linear4.137±2.2634.380±1.4144.312±1.0654.245±0.904
Table 01c
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 150\) for model (04c.01).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none1.149±3.6231.073±1.3410.749±0.6710.539±0.410
linear0.806±3.6810.819±1.4220.521±0.7470.301±0.471
Input \(r\) = 0.003
none4.664±3.4254.240±1.4263.895±0.7943.695±0.559
linear4.326±3.4663.972±1.5813.660±0.9883.463±0.736
Table 02
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 500\) for model (04.02).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none-0.230±2.5480.210±0.954 0.301±0.4780.316±0.300
linear-0.542±2.716-0.001±1.1560.154±0.6590.177±0.445
Input \(r\) = 0.003
none2.603±2.5383.142±1.0783.281±0.6453.335±0.480
linear2.348±2.6602.981±1.2353.162±0.7953.196±0.613
Table 02b
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 150\) for model (04b.02).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none-0.834±1.9230.085±0.918 0.357±0.6230.463±0.520
linear-1.255±2.136-0.126±1.1810.112±0.8750.159±0.759
Input \(r\) = 0.003
none2.293±1.9573.155±1.0243.414±0.7283.516±0.617
linear1.818±2.3372.889±1.3803.121±1.0093.165±0.845
Table 02c
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 150\) for model (04c.02).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none0.196±3.645 0.296±1.3250.249±0.6230.215±0.350
linear-0.123±3.7130.061±1.4160.094±0.7070.084±0.418
Input \(r\) = 0.003
none3.677±3.4373.433±1.3813.322±0.7403.278±0.517
linear3.335±3.4803.137±1.5403.091±0.9313.080±0.678
Table 03
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 500\) for model (04.03).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none-0.073±2.5100.431±0.921 0.512±0.4720.493±0.313
linear-0.972±2.643-0.242±1.1340.028±0.6750.103±0.476
Input \(r\) = 0.003
none3.102±2.6303.484±1.1113.544±0.6633.542±0.498
linear2.232±2.7482.826±1.3163.061±0.8723.135±0.680
Table 03b
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 150\) for model (04b.03).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none-0.078±1.8800.728±0.926 0.953±0.645 1.039±0.552
linear-2.276±2.137-0.670±1.246-0.209±0.963-0.079±0.859
Input \(r\) = 0.003
none3.054±1.9293.808±1.0794.018±0.7924.098±0.680
linear0.788±2.3952.325±1.5102.774±1.1452.897±0.975
Table 03c
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 150\) for model (04c.03).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none0.359±3.716 0.509±1.373 0.443±0.664 0.367±0.394
linear-0.515±3.828-0.187±1.497-0.057±0.776-0.020±0.484
Input \(r\) = 0.003
none3.910±3.4303.672±1.4043.540±0.7773.462±0.548
linear3.016±3.5402.902±1.6312.937±1.0182.971±0.750
Table 04
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 500\) for model (04.04).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none2.177±2.644 3.196±1.189 4.105±0.778 5.251±0.660
linear-1.080±2.723-0.380±1.280-0.623±0.813-0.898±0.617
Input \(r\) = 0.003
none5.596±3.0386.657±1.4327.837±0.9949.371±0.903
linear2.088±3.0362.770±1.5042.552±1.0322.261±0.841
Table 05
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 500\) for model (04.05).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none34.442±6.45631.533±3.85934.083±3.35942.910±3.300
linear-0.825±3.233-0.272±1.722-0.078±1.284-0.003±1.118
Input \(r\) = 0.003
none38.010±7.05535.224±4.25738.041±3.61347.093±3.464
linear1.926±3.346 2.632±1.826 2.908±1.412 3.027±1.284
Table 06
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 500\) for model (04.06).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none-0.748±2.398-0.191±0.916-0.035±0.4840.025±0.321
linear-0.546±2.4920.018±1.071 0.137±0.654 0.134±0.476
Input \(r\) = 0.003
none2.406±2.9382.883±1.2393.023±0.7083.081±0.500
linear2.621±3.0103.111±1.3613.218±0.8553.209±0.655
Table 07
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 146\) for model (04.07).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none-0.952±2.508-0.303±0.901-0.115±0.424-0.046±0.251
linear-0.965±2.617-0.244±1.061-0.046±0.597-0.009±0.417
Input \(r\) = 0.003
none2.438±2.5572.787±1.0782.904±0.6352.959±0.466
linear2.627±2.7232.967±1.3223.051±0.8853.049±0.693
Table 07b
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 146\) for model (04b.07).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none-0.773±1.698-0.153±0.8320.028±0.5740.100±0.484
linear-0.319±1.9550.171±1.118 0.174±0.8580.134±0.759
Input \(r\) = 0.003
none2.345±1.7512.913±0.9543.080±0.6823.148±0.571
linear2.739±2.1813.199±1.3623.201±1.0183.160±0.856
Table 07c
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 146\) for model (04c.07).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none-0.504±3.503-0.169±1.276-0.049±0.593-0.004±0.323
linear-0.582±3.641-0.183±1.439-0.031±0.7420.011±0.449
Input \(r\) = 0.003
none3.170±3.3043.012±1.3342.998±0.7113.000±0.486
linear3.148±3.4643.021±1.6033.027±0.9943.030±0.723
Table 08
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 150\) for model (04.08).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none5.054±2.7894.741±1.1284.106±0.6293.535±0.432
linear2.948±2.8732.792±1.2922.408±0.8442.071±0.661
Input \(r\) = 0.003
none8.045±2.7097.584±1.2747.004±0.8266.540±0.634
linear6.094±2.7995.803±1.4965.501±1.0925.260±0.896
Table 08b
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 150\) for model (04b.08).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none13.919±2.07313.514±1.10013.318±0.79813.269±0.693
linear6.479±2.327 6.174±1.388 6.035±1.085 5.982±0.971
Input \(r\) = 0.003
none17.031±1.97616.655±1.18316.479±0.91016.441±0.801
linear9.528±2.365 9.239±1.567 9.088±1.242 9.015±1.092
Table 08c
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 150\) for model (04c.08).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none8.855±4.0707.104±1.6525.267±0.8833.953±0.561
linear4.726±4.2663.459±1.9222.004±1.1381.107±0.757
Input \(r\) = 0.003
none11.956±3.88510.010±1.7168.293±0.9757.135±0.684
linear7.889±3.907 6.488±1.972 5.227±1.3014.429±0.968
Table 09
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 150\) for model (04.09).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none2.856±2.5872.827±1.016 2.396±0.552 1.966±0.370
linear0.100±2.885-0.070±1.327-0.494±0.819-0.736±0.599
Input \(r\) = 0.003
none5.897±2.8075.687±1.2695.304±0.7754.973±0.570
linear3.493±3.0093.145±1.5152.772±1.0252.554±0.828
Table 09b
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 150\) for model (04b.09).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none19.799±2.26219.328±1.36019.347±1.06319.460±0.950
linear9.009±2.449 8.154±1.565 7.584±1.265 7.292±1.145
Input \(r\) = 0.003
none22.783±2.16722.508±1.37222.666±1.10422.863±0.996
linear11.822±2.62611.105±1.82710.610±1.48010.356±1.313
Table 09c
Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of \(\simeq 150\) for model (04c.09).
Decorrelation model \(A_L\) = 1 \(A_L\) = 0.3 \(A_L\) = 0.1 \(A_L\) = 0.03
Input \(r\) = 0
none5.573±3.8844.208±1.5282.769±0.7891.724±0.469
linear2.919±4.2281.487±1.8490.122±1.008-0.535±0.607
Input \(r\) = 0.003
none8.797±3.7877.182±1.6365.856±0.9044.939±0.603
linear6.232±3.9444.613±1.9003.407±1.1812.774±0.855
\(r\) bias \( imes 10^4\)\(\sigma(r) imes 10^4\)
04.000.3 5.7
04.015.2 6.4
04.021.8 6.5
04.030.4 6.7
04.04-8.3 8.3
04.050.0 15.0
04.061.8 6.6
04.07-0.2 6.0
04.0825.5 8.4
04.09-5.3 8.1
Table 10:
Bias on \(r\), obtained by subtracting the mean of the model 00 (the now negligible algorithmic bias, see Table 00) from each of the 6 complex foreground models, for the case \(A_L\) = 0.1, assuming no decorrelation or linear decorrelation for the Gaussian model. For this Gaussian foreground case, we report a bias based on the absolute value of the sample variance on the mean for \(\simeq 500\) sims, which acknowledges statistical limitations exist even for closed-loop tests calibrated by MC sims.
\(r\) bias \(\times 10^4\)\(\sigma(r) \times 10^4\)\(r\) bias \(\times 10^4\)\(\sigma(r) \times 10^4\)
No decorrLinear decorr
r=0
04.000.2 6.2 0.7 10.2
04.016.8 4.7 5.3 6.4
04.024.0 4.8 2.0 6.6
04.036.1 4.7 0.7 6.7
04.0442.0 7.8 -5.8 8.1
04.05341.8 33.6 -0.3 12.8
04.060.6 4.8 1.8 6.5
04.07-0.2 4.2 -0.0 6.0
04.0842.0 6.3 24.5 8.4
04.0924.9 5.5 -4.5 8.2
\(r\) bias \(\times 10^4\)\(\sigma(r) \times 10^4\)\(r\) bias \(\times 10^4\)\(\sigma(r) \times 10^4\)
No decorrLinear decorr
r=0.003
04.000.6 7.7 0.8 10.2
04.017.0 6.5 5.4 8.5
04.024.1 6.5 2.0 8.0
04.036.7 6.6 1.0 8.7
04.0449.6 9.9 -4.1 10.3
04.05351.7 36.1 -0.6 14.1
04.061.5 7.1 2.6 8.6
04.070.3 6.4 0.9 8.8
04.0841.3 8.3 25.4 10.9
04.0924.3 7.7 -1.9 10.2