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-0.144±2.568-0.061±0.926-0.037±0.447-0.024±0.276
linear-0.172±2.617-0.069±1.020-0.028±0.569-0.012±0.406
Input \(r\) = 0.003
none2.827±2.6602.908±1.0952.944±0.6222.974±0.444
linear2.859±2.8352.940±1.2922.985±0.8073.015±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
none0.379±1.7950.197±0.8800.108±0.5940.098±0.488
linear0.344±1.9960.192±1.0850.136±0.8220.124±0.733
Input \(r\) = 0.003
none3.494±1.8343.277±1.0013.167±0.6923.148±0.563
linear3.419±2.1143.218±1.2423.148±0.9143.137±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-0.167±3.501-0.064±1.263-0.015±0.5810.001±0.316
linear-0.248±3.620-0.101±1.406-0.021±0.7240.009±0.442
Input \(r\) = 0.003
none3.382±3.3863.070±1.3593.013±0.7192.998±0.487
linear3.356±3.5423.064±1.6013.024±0.9733.020±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
none0.913±2.6250.816±0.9610.663±0.4770.538±0.305
linear0.738±2.7260.645±1.1110.489±0.6380.379±0.446
Input \(r\) = 0.003
none3.868±2.6973.759±1.1293.644±0.6633.573±0.486
linear3.724±2.8423.629±1.3143.522±0.8463.458±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
none2.281±2.0001.861±0.9991.707±0.6851.702±0.572
linear1.708±2.1581.295±1.2061.197±0.9181.180±0.805
Input \(r\) = 0.003
none5.461±2.0134.970±1.1194.784±0.7924.774±0.667
linear4.882±2.3274.402±1.4194.273±1.0664.234±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
none1.562±3.6031.225±1.3140.801±0.6490.544±0.401
linear1.240±3.6900.953±1.4170.543±0.7450.296±0.471
Input \(r\) = 0.003
none4.919±3.4894.332±1.4483.922±0.8013.694±0.559
linear4.611±3.5464.069±1.6003.680±0.9913.461±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
none0.367±2.6490.372±0.9830.340±0.4840.316±0.299
linear0.035±2.7900.110±1.1600.153±0.6540.174±0.442
Input \(r\) = 0.003
none3.311±2.6083.346±1.0963.332±0.6523.334±0.480
linear3.019±2.6953.114±1.2293.163±0.7893.192±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
none0.403±2.042 0.447±0.971 0.433±0.6370.468±0.521
linear-0.471±2.196-0.117±1.1800.074±0.8730.152±0.759
Input \(r\) = 0.003
none3.567±2.0803.538±1.0803.493±0.7393.521±0.616
linear2.640±2.3942.910±1.3833.084±1.0113.158±0.846
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
none0.571±3.6340.418±1.3070.286±0.6060.217±0.342
linear0.274±3.7280.171±1.4140.108±0.7060.082±0.418
Input \(r\) = 0.003
none3.897±3.5253.499±1.4163.335±0.7533.273±0.519
linear3.592±3.5773.219±1.5603.105±0.9333.078±0.679
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
none0.611±2.605 0.645±0.953 0.577±0.4820.501±0.314
linear-0.294±2.746-0.102±1.1470.011±0.6730.083±0.476
Input \(r\) = 0.003
none3.879±2.7003.737±1.1313.622±0.6693.551±0.497
linear2.995±2.8022.994±1.3173.050±0.8723.115±0.681
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
none1.129±1.970 1.081±0.970 1.017±0.658 1.039±0.553
linear-1.506±2.178-0.786±1.239-0.327±0.960-0.106±0.859
Input \(r\) = 0.003
none4.292±2.0514.174±1.1404.080±0.8064.097±0.679
linear1.593±2.4452.218±1.5082.657±1.1452.869±0.976
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
none0.741±3.714 0.629±1.356 0.476±0.646 0.366±0.386
linear-0.071±3.861-0.067±1.503-0.054±0.775-0.034±0.484
Input \(r\) = 0.003
none4.136±3.5093.736±1.4333.548±0.7873.452±0.549
linear3.325±3.6302.998±1.6472.941±1.0192.958±0.751
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
none1.657±2.751 2.137±1.185 2.880±0.732 4.452±0.613
linear-1.408±2.845-0.898±1.306-0.861±0.830-1.049±0.633
Input \(r\) = 0.003
none5.077±3.0605.493±1.4166.412±0.9458.429±0.856
linear1.789±3.0912.216±1.5202.270±1.0452.079±0.855
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
none34.859±6.66928.411±4.40128.302±2.77338.323±3.058
linear-0.120±3.526-0.074±1.956-0.026±1.499-0.001±1.308
Input \(r\) = 0.003
none38.368±7.18832.247±4.57631.949±2.97742.605±3.215
linear2.710±3.709 2.897±2.136 3.020±1.667 3.075±1.508
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-0.089±2.525-0.003±0.9610.013±0.5010.028±0.324
linear0.063±2.593 0.145±1.093 0.146±0.6570.130±0.476
Input \(r\) = 0.003
none3.056±2.9643.077±1.2463.074±0.7113.081±0.499
linear3.221±3.0253.242±1.3643.228±0.8563.204±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-0.265±2.549-0.096±0.915-0.053±0.432-0.036±0.252
linear-0.335±2.642-0.113±1.065-0.037±0.597-0.011±0.417
Input \(r\) = 0.003
none3.073±2.6092.996±1.1142.973±0.6592.971±0.473
linear3.188±2.7743.090±1.3333.062±0.8863.048±0.694
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
none0.341±1.8010.180±0.8830.103±0.5890.106±0.484
linear0.262±2.0080.176±1.1180.153±0.8560.131±0.759
Input \(r\) = 0.003
none3.495±1.8563.269±1.0103.161±0.6973.155±0.572
linear3.352±2.2353.209±1.3633.178±1.0193.157±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-0.172±3.479-0.066±1.257-0.015±0.5810.002±0.318
linear-0.264±3.633-0.107±1.432-0.021±0.7400.011±0.449
Input \(r\) = 0.003
none3.382±3.3913.077±1.3643.018±0.7233.002±0.488
linear3.346±3.5533.067±1.6183.033±0.9943.030±0.724
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
none6.028±2.8385.126±1.1394.264±0.6343.573±0.432
linear4.046±2.9343.226±1.3082.522±0.8432.074±0.659
Input \(r\) = 0.003
none8.933±2.7707.949±1.3117.153±0.8476.573±0.639
linear7.110±2.8766.234±1.5185.637±1.0935.281±0.897
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
none14.792±2.19313.347±1.14412.957±0.79813.161±0.687
linear7.807±2.408 6.438±1.391 6.023±1.083 5.971±0.971
Input \(r\) = 0.003
none17.919±2.09216.475±1.22816.094±0.91316.325±0.798
linear10.906±2.4669.530±1.580 9.086±1.242 9.005±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
none9.530±4.0677.390±1.6385.364±0.8643.949±0.550
linear5.523±4.2883.840±1.9182.137±1.1251.119±0.751
Input \(r\) = 0.003
none12.450±3.93510.223±1.7318.349±0.9777.113±0.680
linear8.526±4.000 6.828±1.996 5.359±1.3004.445±0.966
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
none3.502±2.6313.033±1.017 2.455±0.549 1.951±0.367
linear0.367±2.922-0.098±1.317-0.562±0.810-0.828±0.594
Input \(r\) = 0.003
none6.458±2.8025.870±1.2765.348±0.7844.944±0.571
linear3.693±3.0433.074±1.5282.648±1.0262.402±0.823
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
none19.873±2.38018.111±1.39618.249±1.05719.184±0.943
linear9.910±2.520 8.184±1.567 7.542±1.263 7.278±1.145
Input \(r\) = 0.003
none22.833±2.18221.223±1.35321.511±1.07922.573±0.989
linear12.754±2.68511.146±1.82910.570±1.48210.341±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
none6.249±3.9084.528±1.5172.928±0.7741.775±0.464
linear3.642±4.2491.843±1.8420.286±1.001-0.496±0.604
Input \(r\) = 0.003
none9.306±3.8617.442±1.6505.997±0.9034.992±0.602
linear6.798±4.0754.923±1.9403.562±1.1902.814±0.855
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 10.3
04.017.0 4.8 5.2 6.4
04.023.8 4.8 1.8 6.5
04.036.1 4.8 0.4 6.7
04.0429.2 7.3 -8.3 8.3
04.05283.4 27.7 0.0 15.0
04.060.5 5.0 1.7 6.6
04.07-0.2 4.3 -0.1 6.0
04.0843.0 6.3 25.5 8.4
04.0924.9 5.5 -5.3 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 7.8 0.8 10.3
04.017.0 6.6 5.4 8.5
04.023.9 6.5 1.8 7.9
04.036.8 6.7 0.6 8.7
04.0434.7 9.5 -7.2 10.5
04.05290.1 29.8 0.3 16.7
04.061.3 7.1 2.4 8.6
04.070.3 6.6 0.8 8.9
04.0842.1 8.5 26.5 10.9
04.0924.0 7.8 -3.4 10.3