Understanding shapesys modifier

[andrewfowlie]

Summary

I’m trying to understand the shapesys modifer. I’ve read the documentation at https://pyhf.readthedocs.io/en/v0.7.6/intro.html#tab-modifiers-and-constraints

I understand that this modifier contributes a factor to the likelihood

Poisson( naux | gamma naux)

where gamma is the multiplicative modifier and

naux = (b / delta b)^2.

That is, it’s the pmf for a Poisson for naux counts given gamma naux expected counts.

I don’t understand this as naux isn’t in general an integer.

Please can you clarify:

• what is the interpretation of this term as a likelihood function? E.g., do we drop the factorial term in the Poisson pmf, replace it with a gamma function or something else?
• what is the interpretation of this term as a piece of a statistical model? I.e., does this represent a sampling distribution for naux? If so how since the Poisson distribution is a discrete distribution and naux isn’t an integer? Does it represent a prior for the parameter gamma? If so how since it isn’t a density?
• more generally, what motivates this choice?

Many thanks 🙏

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