S4 DC1.0 analysis

  (V. Buza, C. Bischoff, J. Willmert)

In this posting I use our spectral-based analysis framework to arrive at parameter constraints derived from the DC1.0 sim-set, 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 DC1.0 sims.

Notes on the method:

Figure 1:

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 1.0). 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.
Note: The lensing spectrum that I use is the one Julian used for the maps. This unfortunately seems to make the mean of the sims disagree slightly with the expectation values of the model.
Note: The 30 GHz and 40 GHz auto-spectra behave strangely at \(l>200\). This is also noted in Justin's checks of the power spectra he suspects that due to the small number of sims, the noise debiasing is off a bit, and the large suppression factor correction blows up the offset. All the cross spectra with this channels suffer from this as well. To see if this problem affects the final ML histograms, I also do an analysis that is limited to the first five \(l\) bins, and observe no extra bias.

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.

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.

The results of the pager above are summarized in the table below under the DC1.0 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 DC1.0 sims (Fisher, DC1.0). We expect the DC1.0 constraints to be more optimistic than the Science Book results due to idealized nature of the simulations, but we expect good agreement between the DC1.0 contraints and Fisher DC1.0, which we do see up to sample variance (we only have 70 sims, thus \(\sqrt{2/70}\sigma=0.17 \sigma\))

Table 1:
The results of the pager above are summarized in the following table.

\(f_{sky}=0.03\)Fisher (BK scaled)DC 1.0 Fisher (DC 1.0)
\(\sigma_r(r=0, A_L=1.00), \times 10^{-3}\)3.822.612.63
\(\sigma_r(r=0, A_L=0.30), \times 10^{-3}\)---1.131.03
\(\sigma_r(r=0, A_L=0.10), \times 10^{-3}\)0.910.670.56
\(\sigma_r(r=0, A_L=0.03), \times 10^{-3}\)---0.460.38