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±2.561-0.208±1.009-0.046±0.568-0.011±0.406
Input \(r\) = 0.003
none2.126±2.6132.686±1.0812.874±0.6172.964±0.443
linear2.209±2.8012.783±1.2922.963±0.8093.015±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-0.735±1.706-0.146±0.8360.024±0.5770.090±0.487
linear-0.592±1.9270.010±1.073 0.118±0.8210.124±0.733
Input \(r\) = 0.003
none2.358±1.7502.912±0.9463.073±0.6723.139±0.561
linear2.455±2.0303.016±1.2183.125±0.9103.136±0.773
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-0.491±3.518-0.166±1.278-0.050±0.592-0.006±0.321
linear-0.563±3.619-0.182±1.410-0.036±0.7260.009±0.442
Input \(r\) = 0.003
none3.180±3.3063.007±1.3332.992±0.7102.995±0.485
linear3.164±3.4623.016±1.5903.016±0.9753.020±0.706
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±2.5230.592±0.9310.589±0.4710.526±0.306
linear0.090±2.6390.493±1.1000.478±0.6390.386±0.445
Input \(r\) = 0.003
none3.140±2.6093.523±1.0943.569±0.6483.562±0.483
linear3.041±2.7693.468±1.2983.505±0.8463.461±0.655
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
none1.093±1.9081.524±0.9561.647±0.6721.701±0.571
linear0.976±2.1001.276±1.2051.235±0.9201.187±0.805
Input \(r\) = 0.003
none4.245±1.9084.623±1.0624.728±0.7784.775±0.667
linear4.122±2.2644.372±1.4144.306±1.0664.240±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±3.6231.072±1.3420.748±0.6710.538±0.410
linear0.806±3.6810.817±1.4220.519±0.7470.300±0.471
Input \(r\) = 0.003
none4.665±3.4254.239±1.4263.894±0.7943.694±0.559
linear4.327±3.4653.971±1.5813.658±0.9883.461±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-0.261±2.5740.181±0.957 0.285±0.4770.310±0.299
linear-0.565±2.735-0.019±1.1540.149±0.6550.179±0.442
Input \(r\) = 0.003
none2.548±2.5433.106±1.0743.262±0.6423.327±0.478
linear2.301±2.6572.955±1.2273.152±0.7903.196±0.609
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-0.836±1.9230.084±0.918 0.357±0.6230.463±0.520
linear-1.262±2.136-0.129±1.1810.111±0.8750.158±0.759
Input \(r\) = 0.003
none2.291±1.9573.155±1.0243.414±0.7283.516±0.617
linear1.811±2.3372.886±1.3803.120±1.0093.164±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
none0.203±3.646 0.298±1.3250.250±0.6230.215±0.350
linear-0.118±3.7140.061±1.4160.093±0.7070.084±0.418
Input \(r\) = 0.003
none3.683±3.4383.434±1.3813.323±0.7403.278±0.517
linear3.339±3.4813.137±1.5403.090±0.9313.079±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-0.062±2.5130.431±0.922 0.511±0.4720.492±0.313
linear-0.981±2.646-0.257±1.1350.019±0.6750.098±0.476
Input \(r\) = 0.003
none3.115±2.6323.485±1.1123.543±0.6633.541±0.498
linear2.225±2.7512.810±1.3163.050±0.8723.128±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-0.090±1.8800.723±0.926 0.950±0.645 1.036±0.552
linear-2.322±2.137-0.692±1.246-0.222±0.963-0.088±0.859
Input \(r\) = 0.003
none3.043±1.9293.803±1.0794.015±0.7924.095±0.679
linear0.739±2.3952.302±1.5102.760±1.1452.886±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
none0.376±3.721 0.510±1.374 0.443±0.664 0.367±0.394
linear-0.513±3.832-0.202±1.498-0.067±0.776-0.025±0.484
Input \(r\) = 0.003
none3.923±3.4343.673±1.4053.539±0.7773.461±0.548
linear3.013±3.5452.884±1.6322.923±1.0182.963±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
none2.244±2.696 3.288±1.211 4.213±0.791 5.361±0.669
linear-1.301±2.773-0.596±1.304-0.814±0.831-1.065±0.632
Input \(r\) = 0.003
none5.694±3.0606.772±1.4477.961±1.0079.488±0.911
linear1.878±3.0692.550±1.5322.343±1.0532.069±0.856
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
none36.007±6.53631.603±4.50333.657±3.09442.894±3.281
linear-0.830±3.465-0.223±1.934-0.026±1.4910.008±1.298
Input \(r\) = 0.003
none39.519±7.18735.543±4.78037.582±3.34547.098±3.433
linear1.966±3.624 2.715±2.103 3.000±1.662 3.076±1.517
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-0.757±2.397-0.197±0.915-0.038±0.4840.023±0.321
linear-0.552±2.4920.012±1.072 0.132±0.655 0.130±0.476
Input \(r\) = 0.003
none2.396±2.9382.877±1.2393.018±0.7083.077±0.500
linear2.615±3.0103.105±1.3633.212±0.8573.204±0.656
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±2.509-0.303±0.901-0.115±0.424-0.046±0.251
linear-0.965±2.617-0.244±1.062-0.046±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±0.8580.133±0.759
Input \(r\) = 0.003
none2.345±1.7502.913±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±1.440-0.031±0.7420.011±0.449
Input \(r\) = 0.003
none3.170±3.3043.012±1.3342.998±0.7123.000±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
none5.076±2.7904.751±1.1284.112±0.6293.538±0.432
linear3.010±2.8752.832±1.2952.434±0.8462.089±0.663
Input \(r\) = 0.003
none8.067±2.7107.595±1.2757.011±0.8276.545±0.634
linear6.157±2.8025.847±1.4995.532±1.0945.282±0.898
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
none13.922±2.07313.515±1.10013.319±0.79813.270±0.693
linear6.479±2.328 6.171±1.389 6.033±1.086 5.981±0.971
Input \(r\) = 0.003
none17.034±1.97616.657±1.18316.480±0.91016.441±0.801
linear9.528±2.367 9.236±1.568 9.086±1.242 9.014±1.093
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
none8.863±4.0717.107±1.6535.269±0.8843.953±0.562
linear4.735±4.2683.460±1.9242.002±1.1391.106±0.757
Input \(r\) = 0.003
none11.964±3.88610.013±1.7168.294±0.9757.136±0.684
linear7.900±3.908 6.491±1.973 5.228±1.3024.430±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
none2.641±2.594 2.708±1.013 2.324±0.549 1.919±0.367
linear-0.498±2.913-0.437±1.324-0.702±0.811-0.864±0.593
Input \(r\) = 0.003
none5.682±2.7865.563±1.2575.224±0.7674.915±0.565
linear2.911±3.0022.755±1.5042.513±1.0152.367±0.820
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
none19.796±2.26219.327±1.36019.346±1.06319.459±0.950
linear8.986±2.449 8.139±1.565 7.573±1.266 7.282±1.145
Input \(r\) = 0.003
none22.780±2.16722.506±1.37222.664±1.10422.861±0.996
linear11.799±2.62611.089±1.82710.598±1.48010.345±1.314
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
none5.588±3.8874.212±1.5292.770±0.7891.724±0.469
linear2.935±4.2311.490±1.8510.123±1.008-0.535±0.607
Input \(r\) = 0.003
none8.814±3.7917.188±1.6375.859±0.9054.940±0.603
linear6.250±3.9484.619±1.9023.409±1.1812.776±0.856
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 5.2 6.4
04.023.8 4.8 1.9 6.5
04.036.0 4.7 0.7 6.7
04.0443.1 7.9 -7.7 8.3
04.05337.5 30.9 0.2 14.9
04.060.6 4.8 1.8 6.5
04.07-0.2 4.2 -0.0 6.0
04.0842.1 6.3 24.8 8.5
04.0924.2 5.5 -6.6 8.1
\(r\) 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
04.016.9 6.5 5.4 8.5
04.023.9 6.4 1.9 7.9
04.036.7 6.6 0.9 8.7
04.0450.9 10.1 -6.2 10.5
04.05347.1 33.5 0.4 16.6
04.061.4 7.1 2.5 8.6
04.070.3 6.4 0.9 8.9
04.0841.4 8.3 25.7 10.9
04.0923.5 7.7 -4.5 10.2