Maximum likelihood search results for Data Challenge 04 model 0, BK14 mask

2019-01-17 B. Racine

This posting reports the ML search on the DC04d, a new variation of the Data challenge 4, where we generate and re-analyze maps which have the same hit pattern on the sky as in the BK14 analysis
We also report the DC04, DC04b, and DC04c results for comparison.

Introduction

In the current posting, we analyse simulations with the mask used in the BK14 paper (DC04d). The corresponding power spectra are shown here, along with other masks.
We are using a BICEP/Keck-style parametrized foreground model, similarly to this posting, which looked at 04, 04b and 04c for different prior choices.
Only model 00 has been analyzed for now, with 300 simulations.
In the current analysis, we use flat priors on \(\beta\)'s and flat priors on \(A_L\): \(A_L\in[0,2]\).
More information about the sky model, the parametric model and priors can be found in older postings.

In section 1, we show the main results concerning the "r" results, and their dependence on \(A_L\)
In section 2, we show the ML parameters' distributions, including foreground parameters, in the form of histograms.
In section 3, we report tables of r constraints for different sky models, masks, lensing residuals, and with and without decorrelation in the ML search.
In appendix A, we plot the hitcount maps, i.e. masks 04, 04b, 04c and 04d.

1. Summary Plots

Figure 1 shows how the constraints on r evolve for the different observation masks, for sky model 00. Figure 2 shows the evolution of \(\sigma(r)\) as a function of residual lensing \(A_L\) for the 3 masks.

**Figure 1**: Summary of the results for different values of \(A_L\). In red, the analysis of the simulations with r=0.003, in green, the r=0 case. On the left, the case without decorrelation in the parametrization, on the right, with linear-\(\ell\) decorrelation. The outer error bars show the standard deviation \(\sigma\) of the \(N_{sims}\) simulations' ML results (\(N_{sims}\)=150), and the inner error bars show \(\sigma/\sqrt{N_{sims}}\) ; (04 has 1000 realizations and 04b/c/d have only 300).

In figure 2, we show the evolution of \(\sigma(r)\) as a function of \(A_L\).

Comments on Figure 2:

The new 04d mask yields a steeper slope, as expected.

**Figure 2**: Evolution of \(\sigma(r)\) as a function of \(A_L\), for the 3 masks. In blue the circular 3% mask, in green the nominal Chile mask and red, the nominal Pole mask. The error bars are an estimate of the error on the std, estimated as \(\sigma/\sqrt{2*N_{sims}}\). A linear fit is shown as a faded dashed line and the numbers are reported in the legend.

2: Parameter distributions

In figure 3, we report the full distribution of the ML parameters.

Comments on figure 3 (More comments in the case of DC04 can be seen in this posting):

**Figure 3**: Figure representing the ML parameters histograms for model 00.

In the histograms, we report the mean of the distribution as a red line, and the fiducial input value as a **black line** (if defined: see this table). We also report the mean±standard deviation of the distribution.

3: DC4, DC4b and DC4c results table

In the following tables, we report the \(r\) results for the case where all the parameters have generous flat priors.

00: Gaussian foregrounds

The mean values and standard deviations of \(r\) for simulations with simple Gaussian foregrounds are summarized in Table 00, Table 00b and Table 00c, respectively for the circular 3% mask, the nominal Chile mask and the nominal Pole mask.

Figure 1 shows these results in a plot.

Table 00

Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of 476/484 realizations with simple Gaussian foregrounds and fiducial r=0/0.003, for the "CDT" circular idealized f_sky 3% mask (04.00).

Decorrelation model	\(A_L\) = 1	\(A_L\) = 0.3	\(A_L\) = 0.1	\(A_L\) = 0.03
Input \(r\) = 0
none	0.104±2.687	0.033±0.977	0.013±0.480	0.003±0.300
linear	0.062±2.717	0.001±1.045	-0.013±0.573	-0.017±0.406
Input \(r\) = 0.003
none	3.097±2.767	3.019±1.140	3.009±0.654	3.013±0.475
linear	3.111±2.922	3.022±1.311	3.008±0.808	3.013±0.609

Table 00b

Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of 143/146 realizations with simple Gaussian foregrounds and fiducial r=0/0.003, for the nominal Chile mask (04b.00).

Decorrelation model	\(A_L\) = 1	\(A_L\) = 0.3	\(A_L\) = 0.1	\(A_L\) = 0.03
Input \(r\) = 0
none	0.527±1.830	0.293±0.913	0.193±0.640	0.157±0.538
linear	0.470±2.020	0.245±1.094	0.154±0.824	0.124±0.733
Input \(r\) = 0.003
none	3.647±1.866	3.382±1.034	3.265±0.739	3.222±0.614
linear	3.551±2.138	3.278±1.254	3.173±0.919	3.140±0.774

Table 00c

Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of 143/146 realizations with simple Gaussian foregrounds and fiducial r=0/0.003, for the nominal Pole mask (04c.00).

Decorrelation model	\(A_L\) = 1	\(A_L\) = 0.3	\(A_L\) = 0.1	\(A_L\) = 0.03
Input \(r\) = 0
none	0.023±3.645	0.007±1.317	0.022±0.609	0.022±0.331
linear	-0.062±3.757	-0.044±1.440	-0.006±0.728	0.007±0.441
Input \(r\) = 0.003
none	3.502±3.589	3.116±1.442	3.038±0.771	3.013±0.530
linear	3.470±3.726	3.101±1.645	3.036±0.979	3.021±0.705

Table 00d

Mean \(r \times 10^3\) and \(\sigma(r) \times 10^3\) from sets of 143/146 realizations with simple Gaussian foregrounds and fiducial r=0/0.003, for the mask used in the BK14 paper (04d.00).

Decorrelation model	\(A_L\) = 1	\(A_L\) = 0.3	\(A_L\) = 0.1	\(A_L\) = 0.03
Input \(r\) = 0
none	0.218±4.799	0.017±1.645	-0.008±0.697	-0.001±0.322
linear	0.179±4.896	-0.024±1.734	-0.037±0.784	-0.018±0.411
Input \(r\) = 0.003
none	3.921±4.477	3.235±1.657	3.055±0.879	3.002±0.598
linear	3.892±4.492	3.205±1.744	3.035±0.999	2.995±0.713

Appendix A: hitcount maps

As explained here, 04 is the reference mask, with peak value at unity. The other masks have been rescaled to have the same total number of hits (i.e. same sum).

**Figure 4**: Hitcount maps: 04 is the circular 3% mask, 04b is the nominal Chile mask 04c is the nominal Pole mask and 04d is the hitcount used in BK14.