Pk1d covariance improvements #1003
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…l for no_weights but no fit_snr
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Here are the tests I made on the Ohio-mocks: |
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Here are my calculations, I hope it is readable: |
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Ok, from your write up I think you're doing the right thing and keep correlations the same when doing covariance rescaling. I wouldn't just scale the diagonals... Also the non-weighted (i.e. all modes have same weight, forests have different weight depending on how many modes fall in a bin for that particular forest) looks like it's right. It's weird that the weighted covariance wouldn't reproduce the variance (which it should by definition even in the weighted case). Are you sure there's no bug in the calculation? I think normally one would multiply each occurance of P with a weight (for simplicity I'm using sum w=1, here), i.e. var = sum P2 w2, mean = sum P w, Cij = sum wi Pi wj Pj. But you've put additional sqrts for your weights in the cov case (and just insert the final solution for sigma=var**0.5...) I'll have a closer look later... |
| weight2 = 1 / selected_variance_estimated[ipk2] | ||
| covariance_array[index] = covariance_array[index] + selected_pk[ | ||
| ipk | ||
| ] * selected_pk[ipk2] * np.sqrt(weight * weight2) |
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why is the weighting done with a sqrt(weight *weight2) instead of with the weights directly, see other comment
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I'm merging this anyway to allow usage of the existing improvements. @corentinravoux: we'll need to think about exact definitions again at a later time and update the estimators accordingly. The need to rescale does look very weird to me... |
Improvements of the covariance matrix calculation.
In particular, this branch can now compute the covariance matrix with the fit_snr method used to compute mean P1D.
This branch will be used to build the first covariance matrix of the EDR+M2 measurement.
I suggest using this branch to make all the improvements discussed in previous covariance matrix calculations. Do not hesitate to push on this branch if you have any changes.
I perform tests on Ohio EDR-mocks to assess the quality of the covariance matrix. In particular, I compared the error computed in the average calculation (standard deviation) with the diagonal of the covariance matrix:
For the no_weights method, the diagonal is exactly the same by construction. I also verified on paper that the two estimates are theoretically equal.
For the fit_snr method, the error on P1D is not computed with an estimator but with a fitting. It means that theoretically, with the covariance matrix calculation implemented, the error and the diagonal of the matrix are not equal. You will see an attachment showing the difference between those two. I choose to renormalize the diagonal by the error to have something consistent between the error and the diagonal covariance. This choice can be discussed (for example, do we extend this normalization to the full covariance matrix?).
I will also attach the small theoretical calculations I made.