Pseudo-cl's in the covariance computation - pixel window function

[olakusiak]

Hi Namaster team,

I am wondering about the proper treatment of the theory cl’s that go into the covariance computation. If I don’t have any theory power spectra, so I follow the Nicola et al. treatment and the Note in the documentation, and I compute the “pseudo-𝐶ℓ of the associated maps (e.g. computed via compute_coupled_cell()), divided by the same mean mask product”.

However, I am wondering if these pseudo-Cl ’s should in principle be corrected for the pixel window function if they are supposed to represent the “true” power spectra ? I tested it, and this is a small effect for nside=4096, but I was wondering what the correct treatment is. Thank you!

[damonge]

Hi Ola!

no, in this case, since you are computing the pCl that enters the covariance from your own data, you should not correct the result for the pixwin. I am assuming here that, if your data is affected by a pixwin, you will have either passed that pixwin as the beam argument of the corresponding NmtFields, in which case any pixwin deconvolution is taken care of automatically by the corresponding workspaces (optionally, you may be forward-modelling the pixwin in your theoretical prediction, if these C_ells are being used in a likelihood, but in that case you should also not correct the covariance pCls for the pixwin).

To clarify more (hopefully), if you were using a theoretical prediction for the C_ell, instead of your own data, you would need to apply a pixwin to that one before mode-coupling, since this C_ell is meant to contain all the effects that are present in your data.

Does this make sense?

[olakusiak]

Hi David, thank you for your response! Yes, I now add the pixwin as a beam to the corresponding NmtFields (something together with an actual beam), so in this case, if I understand, correctly I never have to worry about the pixwin again (including in the pCl calculation from the same Nmtfields for iNKA for the cov)?

I think it would be super useful to clarify what is meant by the ‘Cl_theory’ in the covariance documentation (that these might need to include the pixwin/beam depending on one’s assumption, whereas I would normally assume that Cl_theory is a theoretical model for the underlying signal)

[damonge]

OK, noted. Luckily we're in the middle of a mild documentation refurbish, so this is good timing ;-)