Currently, to get the prior on N(z), we set the mean to the average of the COSMOS-30-band N(z) and the N(z)s from the different photo-z stacks (see here). I think this should just be the COSMOS-30band N(z), since the CV covariance we use corresponds to the COSMOS-30band sample.

We should check that the get_theory function here produces the same predictions as the one used in LSSLike.

OK, I've had a look at the current code. Here are a few coments:

• In calculate_smooth_s_and_prior.py:
  • We should remember here that the "data" N(z) is the mean of COSMOS N(z) and the photo-z stacks. I think this should just be the COSMOS, but let's leave it as it is and fight it out later. I've opened an issue about this (#1).
  • Can you explain what's going on here and on the next line? It seems like you're assigning all elements the same noise.
  • I have looked briefly over the functions compute_covmat_cv an obtain_smoothing_D, but I haven't checked the formulas. It'd be good to write the formulas used for both of them in the notes so we don't have to rederive them every time. I've open an issue so we don't forget (#2).
  • Can you remind me what the motivation for the specific choice of A_smooth is here?
  • Could you make a plot that shows: a) the COSMOS N(z), b) The N(z)s for the different photo-z codes, c) The error bars associated to P0 and d) The smoothed-out version of N(z) (s_0 in the notes). This is just to get an idea of how all of this looks right now.
  • It's fine for now, but at some point we should add the cross-bin CV covariance here. I've opened an issue (#3).
  • On this line, the following would be faster, because matrix-vector products and equation solving are faster than matrix-matrix products and matrix inversions respectively (although this is probably not a problem in this case):

s_smooth = np.linalg.solve(P0+D, np.dot(P0, s0))

• In create_sacc.py:
  • You should delete this line, right?
  • Have we checked that get_theory is roughly OK? I.e. that it reproduces the same theory curves that the likelihood does? Have we plotted it against the data? I know I coded this up, and checked it roughly, but it would be good to have someone else's eyes on it. Possibly not an urgent issue, so I've opened a separate isue (#4).
  • Have we checked that the numerical derivative we use for Tmat here is roughly converged?

We should remember to add this.

Could we write the equations for the cosmic variance and smoothness contributions to the N(z) covariance in the notes?