Maximum likelihood search results for Data Challenge 02.00 with two different lensing templates

 (C. Umiltà)

Introduction

This posting follows a previous posting in which I run ML searches on 02.00 simulations using a BICEP/Keck-style parametrized foreground model and two different lensing templates LT.

Summary

Previous results showed that while \(\sigma(r)\) decreased, the bias on \(r\) would still be present. As observed in this 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.

The simulations and LT used for this maximum likelihood (ML) searches are presented here. These are a subset of a hundred 02.00 simulations, each with its respective lensing template. Half of these sims have \(r\)=0 and half have \(r\)=0.003. The ideal lensing template is obtained as the difference of lensed and unlensed sims. The Carron LT is obtained is instead estimated from lensing maps directly. We should compare these results with unlensed sims to check the removal of the lensing contribution realization-by-realization. We do not have sims without lensing, but \(A_{lens}\)=0.03 sims have very little lensing contribution. I run the searches with fixed \(A_{lens}\) and no decorrelation; other parameters are set as usual.

Fig. 1 shows, realization by realization, the \(r\) results of ML search. Orange and blue points compare ML searches with and without a lensing template. Without a lensing template, I obtain the blue points. The points in orange are those with the lensing template added: ideally these points should be on the black line.

Figure 1:
Recovered maximum-likelihood r values for 100 sims. The x-axis values come from sims with \(A_{lens}\)=0.03. The y-axis values are derived from sims with \(A_{lens}\)=1 contribution. The unlensed sims have all been analyzed with standard configuration, with fixed \(A_{lens}\). The lensed sims (y-axis values) are analyzed using the same standard configuration with (orange points) and without (blue points) a lensing template.

In Fig.2 I plot an histograms of the distributions. The blue and the orange distributions come from simulations with the same \(A_{lens}\), only with and without the LT in the analysis. The parameters of the distributions are summarized in Table 1.

Figure 2:
Histograms of recovered maximum-likelihood \(r\) for \(A_{lens}\)=0.03 (green), and \(A_{lens}\)=1 with (orange) and without (blue) a lensing template.
Table 1:
Average and std \(\times 10^3\) of \(r\) distributions.
r = 0 r = 0.003
AL=0.03 -0.07±0.37 2.94±0.59
AL=0.1 -0.05±0.56 2.96±0.79
AL=0.3 0.0001±1.10 3.03±1.30
AL=1 0.22±2.83 3.26±2.89
AL=1 + ideal LT -0.03±0.29 2.95±0.46
AL=1 + carron LT -0.07±1.72 3.10±1.75

Plotting the obtained values of \(\sigma(r)\) against \(A_{lens}\) we can determine what the equivalent \(A_{lens}\) is when using Carron's LT. It seems to be around 0.5.

Figure 3:
\(\sigma(r)\) as a function of \(A_{lens}\). Values plotted are those reported in Table 1. Color blue is for \(r=0\) simulations, while red is for \(r=0.003\) simulations. Values for runs that use Carron's LT are shown with triangles and values that use the ideal LT are shown by squares.