We take the BPWF's and multiply them against a theory model to get the expectation values of the bandpowers under that model. If we do this for the model used to generate the mainline simulations we should get an exact match. In previous rounds there was not an exact match as shown by Ben Racine in 20181116_bpbias_study, and extensive kludging was implemented to fix this up, and avoid biases in the model fit parameters (including \(r\)).
Set 06b currently contains only 100 realizations. Set 04 contains 1000.
For the "lLCDM+fg+noise" sims below we get half the number of realizations since the other half contain \(r=0.003\)
Set 04 did not propagate the lLCDM sims so this click is not available below.
In the "normal" plots the red line is the lLCDM expectation and the green line is the lLCDM+foreground expectation. For the "lLCDM only" simset green perfectly overlies red. The blue points are the mean of the sims with the standard deviation divided by \(\sqrt{n}\) as the errorbar, where \(n\) is the number of sim realizations.
The "ratio" plots show the blue points divided by the green expectations with the errorbar also divided down.
The default click shows the ratio for the "lLCDM only" simset. Since this signal is common across all bands the bandpower deviations are highly correlated. The special behavior of the lensing template auto and cross-spectra is expected. Since we don't have "direct" BPWF's for these we fall back to the old method of just scaling by the ratio of the expectation values to the mean of the signal only sims - so this ratio is forced to unity.
Clicking to "lLCDM+fg+noise" we see again see correlated behavior for bandpowers which are signal dominated (by sync, CMB or dust). Clicking to "04" we see there has been a dramatic change versus the previous round. This is because I found and fixed a problem in the BPWF production code. Per \(\ell\) maps are generated, and then rendered with beam smoothing. The spectra of these is then taken in exactly the same way as when the sim maps are analyzed. These per \(\ell\) spectra are then used to construct BPWF's which desribe how each bandpower is "excited" by power at each \(\ell\) on the sky. When the sim maps for S4 are generated we deliberately do include the Healpix pixel window function - they are supposed to be simulated experimental maps as one would get binning timestream into pixels. But the application of the pixel window had been omitted in the BPWF construction. As we see below adding it dramatically improves the situation versus what Ben was finding in his posting linked above.
Also note that the bandpowers are (approximately) \(\chi^2\) distributed but are being plotted below with Gaussian errorbars. In the lowest bandpowers the number of degrees of freedom is limted and the difference can matter. I don't think there is any strong evidence here for remaining unexplained differences between the mean of sims and the BPWF derived expectation values - at any rate things are a whole lot better than they were for the 04 round.
[Note added 2020 Sept 25: the plots below are for 4325 interative LT set - although it makes little difference.]
[Note added 2020 Sept 28: after the plots below were made we updated to "empirical supfac" on all spectra - not just LT spectra. This causes the "LCDM-only" plot to go to unity for all spectra. This update is necessary to avoid bias on the ML search results found here.]
| Figure 1 | Mean of Sims versus Expvals Pager |
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