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
none0.104±2.6870.033±0.9770.013±0.480 0.003±0.300
linear0.062±2.7170.001±1.045-0.013±0.573-0.017±0.406
Input \(r\) = 0.003
none3.097±2.7673.019±1.1403.009±0.6543.013±0.475
linear3.111±2.9223.022±1.3113.008±0.8083.013±0.609
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
none0.527±1.8300.293±0.9130.193±0.6400.157±0.538
linear0.470±2.0200.245±1.0940.154±0.8240.124±0.733
Input \(r\) = 0.003
none3.647±1.8663.382±1.0343.265±0.7393.222±0.614
linear3.551±2.1383.278±1.2543.173±0.9193.140±0.774
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
none0.023±3.645 0.007±1.317 0.022±0.609 0.022±0.331
linear-0.062±3.757-0.044±1.440-0.006±0.7280.007±0.441
Input \(r\) = 0.003
none3.502±3.5893.116±1.4423.038±0.7713.013±0.530
linear3.470±3.7263.101±1.6453.036±0.9793.021±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
none1.176±2.7450.926±1.0090.729±0.5050.579±0.324
linear0.990±2.8260.725±1.1300.501±0.6370.343±0.451
Input \(r\) = 0.003
none4.150±2.8273.879±1.1893.715±0.7063.613±0.526
linear3.993±2.9493.717±1.3383.541±0.8473.438±0.657
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
none2.450±2.0411.970±1.0411.783±0.7451.717±0.634
linear1.824±2.1761.303±1.2061.118±0.9181.059±0.812
Input \(r\) = 0.003
none5.637±2.0545.084±1.1624.857±0.8474.768±0.716
linear5.004±2.3444.414±1.4214.202±1.0704.130±0.921
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
none1.808±3.7401.334±1.3560.860±0.6640.564±0.404
linear1.501±3.8241.056±1.4430.576±0.7470.276±0.474
Input \(r\) = 0.003
none5.072±3.6784.402±1.5263.957±0.8543.695±0.600
linear4.786±3.7274.148±1.6473.714±0.9993.459±0.739
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
none0.608±2.7620.468±1.0320.390±0.5160.336±0.323
linear0.273±2.8770.181±1.1740.157±0.6530.141±0.448
Input \(r\) = 0.003
none3.608±2.7253.470±1.1483.401±0.6903.363±0.518
linear3.307±2.7833.206±1.2433.176±0.7883.165±0.611
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
none0.583±2.090 0.565±1.018 0.529±0.704 0.516±0.590
linear-0.338±2.215-0.112±1.180-0.009±0.8740.041±0.768
Input \(r\) = 0.003
none3.754±2.1273.666±1.1253.598±0.7943.568±0.665
linear2.781±2.4112.920±1.3842.999±1.0193.042±0.868
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
none0.789±3.7800.504±1.3580.327±0.6290.225±0.350
linear0.512±3.8630.257±1.4420.131±0.7080.066±0.421
Input \(r\) = 0.003
none4.025±3.7283.547±1.5053.352±0.8143.259±0.566
linear3.749±3.7663.288±1.6073.132±0.9413.073±0.683
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
none0.872±2.726 0.754±1.004 0.639±0.515 0.534±0.340
linear-0.019±2.847-0.015±1.162-0.001±0.671-0.011±0.482
Input \(r\) = 0.003
none4.180±2.8173.871±1.1813.702±0.7033.593±0.527
linear3.309±2.8903.104±1.3273.049±0.8733.025±0.696
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
none1.311±2.015 1.206±1.018 1.110±0.728 1.067±0.627
linear-1.363±2.191-0.837±1.237-0.594±0.964-0.480±0.874
Input \(r\) = 0.003
none4.480±2.0984.306±1.1894.176±0.8714.113±0.739
linear1.744±2.4592.171±1.5082.387±1.1552.491±1.004
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
none0.960±3.8670.716±1.4100.516±0.670 0.365±0.395
linear0.204±4.0020.044±1.532-0.035±0.776-0.092±0.487
Input \(r\) = 0.003
none4.264±3.7093.784±1.5213.560±0.8463.423±0.595
linear3.523±3.8083.100±1.6852.974±1.0242.918±0.760
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
none1.410±2.870 1.491±1.220 1.527±0.721 1.536±0.521
linear-1.460±2.951-1.110±1.324-0.961±0.835-0.861±0.651
Input \(r\) = 0.003
none4.814±3.1604.757±1.4554.783±0.9424.798±0.755
linear1.744±3.1811.976±1.5322.118±1.0362.221±0.851
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
none34.336±6.86326.576±4.36923.450±2.69823.144±2.513
linear0.182±3.665 0.036±2.013 0.006±1.511 -0.013±1.318
Input \(r\) = 0.003
none37.838±7.30830.288±4.52126.711±2.79026.610±2.574
linear3.020±3.835 3.029±2.186 3.054±1.689 3.047±1.524
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
none0.166±2.6550.091±1.0160.059±0.5370.045±0.351
linear0.300±2.7040.211±1.1200.159±0.6610.129±0.477
Input \(r\) = 0.003
none3.311±3.0643.178±1.2903.126±0.7413.098±0.527
linear3.456±3.1103.313±1.3863.244±0.8593.203±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-0.005±2.6530.005±0.961 0.003±0.466 -0.003±0.287
linear-0.093±2.725-0.046±1.081-0.028±0.598-0.024±0.417
Input \(r\) = 0.003
none3.318±2.7183.103±1.1693.040±0.7073.016±0.525
linear3.407±2.8633.156±1.3533.073±0.8883.040±0.698
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
none0.497±1.8420.289±0.9270.200±0.6540.167±0.551
linear0.351±2.0240.177±1.1170.111±0.8560.090±0.769
Input \(r\) = 0.003
none3.658±1.8953.387±1.0513.269±0.7533.223±0.629
linear3.447±2.2493.213±1.3643.131±1.0243.109±0.874
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
none0.021±3.621 0.006±1.309 0.022±0.607 0.022±0.332
linear-0.078±3.761-0.053±1.457-0.009±0.7420.006±0.451
Input \(r\) = 0.003
none3.505±3.5983.125±1.4513.044±0.7803.015±0.535
linear3.462±3.7373.103±1.6603.042±0.9993.029±0.727
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
none6.391±2.9425.310±1.1804.399±0.6613.687±0.457
linear4.446±3.0333.428±1.3332.612±0.8442.015±0.648
Input \(r\) = 0.003
none9.271±2.8808.130±1.3667.288±0.8936.675±0.688
linear7.486±2.9816.441±1.5475.753±1.0975.286±0.894
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
none14.917±2.23813.291±1.19112.503±0.85712.165±0.728
linear8.009±2.432 6.542±1.394 5.999±1.078 5.816±0.969
Input \(r\) = 0.003
none18.046±2.13816.414±1.27315.601±0.96915.241±0.847
linear11.119±2.4939.648±1.588 9.080±1.244 8.874±1.098
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
none9.937±4.2187.602±1.6915.479±0.8863.941±0.549
linear6.008±4.4344.136±1.9522.320±1.1191.181±0.728
Input \(r\) = 0.003
none12.752±4.11410.388±1.8078.421±1.0307.036±0.717
linear8.920±4.193 7.102±2.053 5.551±1.3094.532±0.957
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
none3.831±2.7323.192±1.0552.568±0.573 2.051±0.390
linear0.698±3.0100.068±1.342-0.439±0.824-0.715±0.608
Input \(r\) = 0.003
none6.760±2.8906.025±1.3195.464±0.8215.044±0.613
linear3.997±3.1393.237±1.5672.776±1.0502.524±0.840
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
none19.884±2.43117.656±1.44916.630±1.11416.189±0.968
linear10.066±2.5428.206±1.568 7.465±1.258 7.174±1.145
Input \(r\) = 0.003
none22.840±2.21720.737±1.38119.777±1.10219.372±0.993
linear12.916±2.70311.174±1.83010.499±1.49010.243±1.335
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
none6.648±4.0704.759±1.5723.111±0.7991.950±0.480
linear4.070±4.3922.103±1.8770.482±1.007-0.357±0.599
Input \(r\) = 0.003
none9.608±4.0427.636±1.7186.168±0.9435.189±0.639
linear7.136±4.2775.158±2.0073.763±1.2162.976±0.861
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 6.5 0.7 10.5
04.017.2 5.0 5.1 6.4
04.023.8 5.2 1.7 6.5
04.036.3 5.2 0.1 6.7
04.0415.1 7.2 -9.5 8.4
04.05234.4 27.0 0.2 15.1
04.060.5 5.4 1.7 6.6
04.07-0.1 4.7 -0.2 6.0
04.0843.9 6.6 26.2 8.4
04.0925.6 5.7 -4.3 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
04.000.7 8.2 0.9 10.5
04.017.1 7.1 5.3 8.5
04.023.9 6.9 1.7 7.9
04.036.9 7.0 0.4 8.7
04.0417.7 9.4 -8.9 10.4
04.05237.0 27.9 0.5 16.9
04.061.2 7.4 2.4 8.6
04.070.3 7.1 0.6 8.9
04.0842.8 8.9 27.4 11.0
04.0924.6 8.2 -2.3 10.5