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Table 3:

Errors on cosmological parameters for three exemplary data sets with different photometric redshift errors. Top: ratios rF and rb for the three data sets considered. Bottom: marginalized statistical errors $\sigma $, biases b, total errors $\sigma _{\rm tot}$, and $b_{\rm rel}$ for every cosmological parameter, shown for both original and nulled data sets.
Set $\sigma _{\rm ph}$ $f_{\rm cat}$ $r_{\rm out}$ Nulling rF rb
1 0.03 0.01 0.007 (C) 0.438 0.026
2 0.05 0.05 0.032 (B) 0.475 0.039
3 0.07 0.10 0.060 (B) 0.465 0.028

The parameters specifying the photometric redshift errors and the nulling variant used are given. The offset of outliers is fixed at $\Delta _z=1.0$ for all sets. The linear alignment model has been used throughout as systematic, as well as the weighting scheme of Sect. 5.3. Note that set no. 2 is the underlying data for the results of Fig. 14.

Set Par. Original data Nulled data Ratios
    $\sigma $ b $\sigma _{\rm tot}$ $b_{\rm rel}$ $\sigma $ b $\sigma _{\rm tot}$ $b_{\rm rel}$ $\frac{\sigma_{\rm null}}{\sigma_{\rm orig}}$ $\left\vert\frac{b_{\rm null}}{b_{\rm orig}}\right\vert$
1 $\Omega _{\rm m}$ 0.008 -0.137 0.137 -16.921 0.023 -0.003 0.023 -0.137 2.849 0.023
  $\sigma _8$ 0.012 0.166 0.167 14.290 0.030 0.004 0.030 0.125 2.557 0.022
  h100 0.104 0.109 0.151 1.042 0.213 -0.001 0.213 -0.003 2.043 0.006
  $n_{\rm s}$ 0.014 -0.012 0.018 -0.882 0.036 -0.001 0.036 -0.029 2.615 0.086
  $\Omega_{\rm b}$ 0.015 -0.032 0.035 -2.032 0.031 -0.001 0.031 -0.045 1.989 0.044
  w0 0.078 -1.231 1.233 -15.845 0.247 -0.034 0.249 -0.136 3.173 0.027
  wa 0.250 3.123 3.133 12.486 0.737 0.097 0.743 0.132 2.946 0.031
2 $\Omega _{\rm m}$ 0.009 -0.136 0.136 -15.674 0.025 0.003 0.025 0.140 2.830 0.025
  $\sigma _8$ 0.012 0.165 0.166 13.316 0.031 -0.002 0.031 -0.057 2.510 0.011
  h100 0.109 0.095 0.145 0.871 0.203 -0.042 0.207 -0.209 1.859 0.447
  $n_{\rm s}$ 0.014 -0.014 0.020 -0.973 0.033 0.003 0.033 0.075 2.352 0.181
  $\Omega_{\rm b}$ 0.016 -0.034 0.038 -2.101 0.030 -0.002 0.030 -0.084 1.831 0.073
  w0 0.085 -1.225 1.228 -14.486 0.262 0.067 0.270 0.254 3.094 0.054
  wa 0.271 3.132 3.143 11.559 0.765 -0.109 0.773 -0.143 2.825 0.035
3 $\Omega _{\rm m}$ 0.010 -0.135 0.135 -14.090 0.026 -0.002 0.026 -0.075 2.758 0.015
  $\sigma _8$ 0.014 0.164 0.164 12.066 0.033 0.005 0.034 0.145 2.466 0.030
  h100 0.116 0.079 0.140 0.676 0.218 -0.042 0.222 -0.194 1.879 0.538
  $n_{\rm s}$ 0.015 -0.016 0.022 -1.100 0.037 -0.002 0.037 -0.065 2.458 0.145
  $\Omega_{\rm b}$ 0.017 -0.038 0.041 -2.157 0.032 -0.005 0.032 -0.168 1.828 0.142
  w0 0.095 -1.211 1.215 -12.773 0.283 0.021 0.284 0.073 2.986 0.017
  wa 0.302 3.127 3.142 10.360 0.832 0.042 0.833 0.050 2.755 0.013

The last two columns show the ratios of statistical errors and biases before and after nulling.


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