In a previous study I run ML searches on DC02 sims with and without using the lensing template. Quoting from my old posting "(...) the mean of the simulations does not correspond to the exvals of the model: this could be the reason of the observed bias in the recovered r. For this reason in all simulations I subtract to the simulations the mean bias, i.e., the difference between the expectation value and the mean of the sims. The bias in r is largely removed by subtracting the mean of the sims."
When running this on DC06 sims we observed the same bias (see this posting for more details). clem suggested that this is due to forcing the mean of LT for the expval values, while not doing the same for all BB spectra. In fact, when forcing the mean on all spectra, the bias disappear.
In the figure below I histogram the result for ML search on \(r\) for both \(06b\) and \(032\) DC, with and without the lensing template in the search. You can see that adding the lensing template tightens the distribution. For DC \(02\) we have two templates: the ideal lensing template is obtained as the difference of lensed and unlensed sims, while the Carron LT is obtained is estimated from lensing maps directly. For DC \(06b\) we have an additional template in which the reconstruction also includes foregrounds.
The table below summarizes mean and 1-\(\sigma \) values for the histograms (only using 100 sims for both DC \(02\) and \(06b\)). Values are multiplied by 1000 for readability. When using LT, the distribution tightens in DC \(06b\) with respect to DC\(02\). This is not the case when ignoring the LT.i Adding (Gaussian) foregrounds to the reconstruction does not seem to affect the results.
|DC \(02\), no LT||\( 0.0 \pm 2.8\)||\( 2.9 \pm 2.2\)|
|DC \(06b\), no LT||\( 0.5 \pm 3.3\)||\( 4.2 \pm 3.4\)|
|DC \(02\), ideal LT (4331)||\( -0.03 \pm 0.30\)||\( 2.95 \pm 0.46\)|
|DC \(06b\), ideal LT (4326)||\(-0.026 \pm 0.078\)||\( 3.12 \pm 0.32\)|
|DC \(02\), Carron's LT (4333)||\(0.1 \pm 1.7\)||\(3.1 \pm 1.7\)|
|DC \(06b\), Carron's LT (4325)||\(-0.15 \pm 0.47\)||\(3.20 \pm 0.63\)|
|DC \(06b\), Carron's LT with fg (4327)||\(-0.04 \pm 0.51\)||\(3.15 \pm 0.64\)|