S4 DC 01.xx analysis, v2

In this posting, similar to this previous analysis (over just 70 sims), I use our spectral-based analysis framework to arrive at parameter constraints derived from the DC 01.xx sim-sets, and compare the results to the CMB-S4 science book contraints (which were based on scaling the BICEP/Keck covariance matrix), as well as a new Fisher calculation which uses a BPCM derived from the DC 01.xx sims.

Notes on the method:

• We use the DC 01.xx sim-sets (cmb + dust + sync + noise)
• Use the BICEP/Keck multi-component spectral-based likelihood framework.
• Use a pure-B estimator (J. Grain et al, Phys. Rev. D. 79,12315) to calculate all the auto and cross spectra.
• Use a global ML peak search (of similar dimensionality as in the Science Book Fisher forecasts, bar a dust decorrelation parameter) to obtain recovered ML histograms. The standard deviations of histograms offer a measure of the constraining power in our dataset. The means of histograms offer a measure of bias.

Differences from the previous analysis:

• In the previous analysis, the bpwf included response below \(l<30\), but our data challenge maps were explicitly constructed without signal or noise power below \(l=30\). So if one would have naively used these window functions, the model expectation values would have predicted significantly more power in the first bin than we saw from the sims. To fix this, Colin suggested zeroing the bandpower window functions below \(l=30\), renormalizing them, and folding that normalization factor into the suppression factors. One also then applied that normalization factor to all of the sim bandpowers.
• Clem said that he did not like this solution, and that the proper place to account for this truncation was in the theory model spectra. This current analysis does just that by zero-ing the theory spectra below \(l<30\). The functions that were changed are: like_getexpvals.m and model_rms.m.

Figure 1:

mean(sim):
The green line corresponds to the model expectation values calculated according to the fiducial theory model used for the CMB-S4 Sciencebook forecasts (and in Data Challenge 01.xx). This model includes dust, sync, and lensed-CMB, as described on the Data Challenges page, and this forecasting posting. The blue line corresponds to the mean of the signal + noise sims.


var(simd):
The green line shows variances obtained from the fiducial model BPCM (which is formed from A_L=1 + noise sims, and then scaled to the appropriate theory model). The blue line shows variances calculated directly from the signal + noise sims.

mean(noi):
The green line shows the input baseline \(N_l\) levels as presented in this posting and as used for the CMB-S4 forecasting. The blue line shows the mean of the noise-only simulations.
Note: As we can see, while the noise sims are what is described on the Data Challenge page, the blue line is somewhat higher than the green. This comes from the weight mask. The uniform depth region at the center of the field has noise that exactly matches the \(N_l\) from the posting above, but the noise increases near the edge of the field. This does mean that the net \(N_l\) is higher than the model, but how much higher will depend on the weight mask that one uses. This will not have a biasing effect on our parameters, since in the analysis the \(N_l\)'s are calculated directly from the sims, but it will have a net parameter constraint degradation since the sims have a higher level of noise.

ML hist (9 bins/5 bins):
The blue histograms are the recovered ML values with the red line marking the recovered mean, and the black line marking the input model values. Constraints on all the parameters, as well as the recovered means, are summarized in their respective legends.

Note on the mean of the \(r_{ML}\) distributions: Compared to the previous analysis (over just 70 sims), the biases appear to have gotten larger for \(A_L=0.1\) or larger. This is a bit puzzling, since there should be only a difference in technique. If I compare the recovered ML peaks for r for the first 70 realizations (for the \(A_L=1.0\) case) between the current analysis and the previous one, I see the following histogram.

Note on the width of the \(r_{ML}\)distributions: The results of the pager above are summarized in the table below under the DC01.00 column. As mentioned, I compare the results to the CMB-S4 science book contraints, based on scaling the BICEP/Keck covariance matrix (under the Fisher, BK scaled column), and perform a new Fisher calculation which uses a BPCM derived from the DC 01.00 sims (Fisher, DC 01.00). In addition to this, I also add the values obtained from the previous analysis (over just 70 sims). We expect the DC 01.00 constraints to be more optimistic than the Science Book results due to idealized nature of the simulations, but we expect good agreement between the DC 01.00 contraints and Fisher DC 01.00 up to sample variance (we have 1000 sims, thus \(\sqrt{2/1000}\sigma=0.045 \sigma\)).