mean(simd):
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.
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.