Unsure of doc vs implementation

[sambklein]

In the Modifiers and Constraints table the MC stat uncertainty is shown to be parameterised by $\delta^2_b$ in the units of the rate in the bin. So I thought I should pass as input data $\delta^2_b / \nu_{b}$, but this didn't give sensible results or match a simple example I built from scratch. Am I doing something wrong in my cross checks?

Everything works fine if I pass just the unscaled standard deviation $\delta_b$ instead of the scaled variance. I think the tagged line below actually converts to the scaled variance?

pyhf/src/pyhf/modifiers/staterror.py

Line 95 in adddb07

(modifier_data['data']['uncrt'][binnr] / nomsall[binnr]) ** 2

If I'm correct (dubious) I think the constraint term should be $\prod_b\mathrm{Gaus}\left(a_{\gamma_b} = 1\middle|,\gamma_b,\delta_b / \nu_b\right)$? And the input should be $\delta_b = \sqrt{\sum_s\delta^2_{sb}}$?

[alexander-held]

I think you're correct and the width of the Gaussian in the documentation is wrong. For the question of what you actually should put into the modifier in your model: it should be the absolute statistical uncertainty for a given sample, so no scaling needed. See also #1018.

[sambklein]

Ok great, thanks! I'll also make a comment on the issue