Implement pdf+th error for yadism grids about nnusf

[Radonirinaunimi]

This is indeed definitely true. Actually, right now the matching of the NNUSF to the Yadism predictions at high-Q2 only account for the PDF uncertainties. This will be important when Alfonso adds uncertainties to his plots. This, I forgot to mention when we chatted this morning about the missing bit.

ATM, I am not fully certain on how to best account for this here:

nnusf/src/nnusf/theory/predictions.py

Lines 140 to 146 in f573beb

	def combined_error(
	grid: pineappl.grid.Grid,
	pdf: str,
	prescription: list[tuple[float, float]],
	xgrid: npt.NDArray[np.float_],
	reshape: Optional[bool] = True,
	) -> npt.NDArray[np.float_]:

[Radonirinaunimi]

I haven't read this paper yet but would this method be consistent with what we do in the fit where PDF and Theory errors are accounted for by combining their covariance matrix in quadrature?

[RoyStegeman]

Yes sorry it's probably a bit too cumbersome for now so I removed the comment. Should indeed be consistent with what we usually do except that it accounts for the full correlations.

[Radonirinaunimi]

I see. There should be an easy way to do this, something along the lines of computing the the up and down shifts of the theory variations wrt to the central value and somehow add these information to the replicas.

[RoyStegeman]

Yes that's the default scale variations solution right; In which the observable shift observed upon performing a factor 1/2 and 2 shift of the scales is assumed equal to 1sigma (taking the largest observed shift when varying multiple scales). Then we can indeed sum the variances as you say.

I'm still not a huge fan of scale variations, but unfortunately it's the best/all we really have. Might be good to confirm with Juan before we proceed.

[Radonirinaunimi]

Sorry for the late reply, we had a QCD-EFT group meeting earlier.

Yes that's the default scale variations solution right; In which the observable shift observed upon performing a factor 1/2 and 2 shift of the scales is assumed equal to 1sigma (taking the largest observed shift when varying multiple scales). Then we can indeed sum the variances as you say.

I'm still not a huge fan of scale variations, but unfortunately it's the best/all we really have. Might be good to confirm with Juan before we proceed.

Me neither! However that's the best we could do so far. Currently tough, we are already including theory errors with the 7-point scale variation in the fit as agreed with Juan in #47.

The problem I was seeing before was: how to properly account for these theory errors when dumping the Yadism predictions into a LHAPDF grid such that we are consistent with what we do in the fit? But now I think I might have an idea that I'm testing right now.

[Radonirinaunimi]

Nvm, what I intended to do does not work. Back into the drawing board.

[Radonirinaunimi]

Closing this as per discussion in the Slack.