Bandpower bias study

  B. Racine

In this posting, we show that the mean of the simulations deviates from the expectation value of the input fiducial model. We then try two corrections, one multiplicative and one additive. This reduces the bias at ML parameter levels for some parameters but there is still some significant deviation.

In the DC4 ML search results, we still see residuals at the parameter levels, especially for \(A_L\) and for the \(\alpha\)'s. Here we check if the bias is present at the bandpower level.
In this posting, we see that when inputing some expectation value corresponding to some given parameters, the ML search recovers the proper values.

1: Bandpower bias

We compute the bandpower deviation, shown in figure 1 as follows:

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Figure 1: Bandpower deviation, before and after additive or multiplicative bias removal.

2: Bias removed simulations: ML results.

We then correct each simulation's bandpower before using the multicomponent ML search, either by subtracting (mean(bp_{sims}) - bp_{in})), or by dividing them by (mean(bp_{sims})/bp_{in})). This forces the mean of the sims to fit the input fiducial model. We also ran a case where we fixed the \(\alpha\) to their fiducial values in the ML search.

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Figure 2: Histograms and bias significance, before and after additive or multiplicative bias removal.

We also plot the -2*log(Likelihood) value for all the 1000 simulations (r=0 and r=0.003 altogether) for the different values of \(A_L\). We see that the distribution shifts slightly to lower numbers when we remove the additive bias, but goes bad when we use the additive bias.

Figure 3: -2 log(Likelihood) distribution of the ~1000 distributions. .