DC05.00 closed loop exercise

2019-04-11 B. Racine

In this posting we run the maximum likelihood search on the DC5, which mimics the BK15 dataset.

1. Introduction

This posting is a quick closed loop test where we analyze a BK15 like data challenge.
In this previous posting, we obtained noise parameters from the published BK15 bandpowers.
In this other posting, we showed the power spectra (final pager) of the simulations generated using these parameters, for the Gaussian foreground case (05.00).

Note that an analysis of the BK only data was reported in the BK15 paper for the CosmoMC analysis, see for instance figure 18 in the appendix.

2. Details on the analysis.

Here we fix the lensing amplitude to 1, and we don't allow for decorrelation. We also impose the Planck priors on the \(\beta\) parameters (see table 1).
There are a few notable differences between the BK15 simulations and the 05.00 ones:

1. The bandpasses used in 05.00 are tophat bandpasses, with bandwidth defined in this posting.
2. The BK15 simulations don't contain any synchrotron and have a slightly lower dust amplitude (see table 1).
3. The lensing power spectrum used is not exactly the same.
4. The S4 sims have no power below \(\ell\) of 30, whereas the BK ones have some, which gets filtered by the data processing.

Table 1: Here we report for each parameters, the fiducial values used in the simulations, as well as the prior used in the ML search.
	BK sims	S4 sims	Priors for ML search
\(r\)	0	0	Flat: [-0.5,0.5]
\(A_d\) [\(\mu K^2\)]	3.75	4.25	Flat: [-2,150]
\(\beta_d\)	1.6	1.6	Flat: [0.8,2.4] and Gaussian \(\mathcal{N}(1.6,0.1)\)
\(A_s\) [\(\mu K^2\)]	0	3.8	Flat: [-2,15]
\(\beta_s\)	NA	-3.1	Flat: [-4.5,-1.5] and Gaussian \(\mathcal{N}(-3.1,0.3)\)
\(\alpha_d\)	-0.4	-0.4	Flat: [-1,0]
\(\alpha_s\)	NA	-0.6	Flat: [-1,0]
\(\epsilon\)	0	0	Flat: [-1,1]

3: Parameters histograms

In Figure 1, we report the histograms of 8 free parameters, for the 499 BK15 simulations, as well as for the 150 (r=0) simulations

Comments on the figure:

For the BK15 499 sims, we have \(10^3 \sigma(r) = 32.39 \pm 1.02 \), where the standard error on the \(\sigma(r)\) is \(\sigma(r)/\sqrt{2*N_{sims}}\).
For the S4 05.00 150 sims, we have \(10^3 \sigma(r) = 38.22 \pm 2.21 \).

**Figure 1**: In the histograms, we report the mean of the distribution as a red line , and the fiducial input value as a **black line**. We also report the mean±standard deviation of the distribution.