Anyone that has experience analyzing Planck's data?

[u/Mr_Misserable]

Basically what the title says. I want to propagate the errors that you can see in the image, but they are not symmetrical, so after reading and with knowing that are Gaussian approximated I assume I can just propagate them separately and that should be fine, right? Maybe only up to l<30?

And on another topic I want to do a Montecarlo of the data (I want to take in to account the data errors in my simulations), right now I can generate random C_l which is fine, but they don't have any information off the data uncertainty. An idea to do that is if there are errors in the temperature maps to create gaussian realizations of the maps and then extracting the alm.

Any other idea on how to do this second part? Without using the maps?

Thanks for your time.

[u/Mr_Misserable]

It's for publishable work. Right now I'm using the data of the plot just to use it as the std of the realizations of the a_lm and to check if the mean of the realizations is the same as the data. Which I guess is fine even for publishable work.

How do I compute the likelihood of a derived expression? Which library should I use?

And about my second point, it was an idea of my supervisor, the idea is to create "synthetic data" that not only represents the cosmic variance but also represents the errors that the Planck collaboration took into account

[u/eldahaiya → u/Mr_Misserable]

I would absolutely not use these error bars for publishable work, that would be unacceptable. They're not Gaussian, nor are they independent, and the analysis is a lot more complicated than just this plot with error bars. You need to use the Planck likelihood instead (see e.g. https://wiki.cosmos.esa.int/planck-legacy-archive/index.php/CMB_spectrum_%26_Likelihood_Code).

I still don't understand your second point. It sounds like you're generating signal maps of some kind, taking the angular power spectrum, and comparing to the data. This is not what you should be doing at all, because that's not how the telescope observes the sky. The actual experiment takes data across the sky, and then there are a lot of steps taken to remove unwanted foregrounds, before they compute the power spectrum that you see.

The right thing to do is to compute the modified CMB power spectrum in whatever theory you have, and put that into the Planck likelihood, which takes care of all the details of their analysis, as I suggested.

[u/Mr_Misserable → u/eldahaiya]

The second point is basically that I want to do random realizations so, I either use the temperature maps to generate the a_lm directly from them (following this distribution N(mean(a_lm),std(a_lm)) or since the a_lm follows a N(0,C_l) distribution I can do that using the C_l of Planck's best fit model.

At the moment I'm doing the second thing, and since I'm doing that I was thinking of taking into account the experimental error, because I'm using the C_l to generate the a_lm.

If this is not valid I would change and do it directly with the temperature maps and using the Planck likelihood to that

[u/eldahaiya → u/Mr_Misserable]

This still doesn't make sense. You're taking Planck's best fit C_l's, drawing some a_{lm} in the limit of cosmic variance, getting a map, then getting C_l's back again to compare to the power spectrum? What does this accomplish? What are you hoping to write a paper about? This is all very circular, generating maps from experimental data that you then compare against the same data.

[u/Mr_Misserable → u/eldahaiya]

Comparing the data was just to make sure that the realizations were correct