Nuisance parameter combinations in HistFactory


i was trying to find a resource that describes how pulls of different nuisance parameters are combined.

Say i am just looking at one bin with nominally 100 events. Now i have two nuisance parameters.
At their +1 uncertainty the first one predicts 105 from the shape component and 110 from the normalization effect.

With the other predicting 98 and 108 respectively.

If both of them are set to their +1 level, what would the final number of events be?

I have looked at the histfactory note and the equation of interest for me there should be equation (6), right?

Then the individual components depend on the chosen interpolation scheme, right?

For example, equation 14 shows that, for linear interpolation, different uncertainty components are summed…

Meanwhile, equation 17 shows that for exponential interpolation they are multiplied.

The current defaults are polynomial interpolation with exponential or linear extrapolation.

Equation 24 shows that for the exponential extrapolation, the combination uses the product. However, i do not know how it works for linear extrapolation.

Is it also fine to assume that these values still hold in current releases? Or is there someplace in the code that i can look to verify these?


Dear @JanEric ,

Thanks for reaching out to the forum! I believe @moneta or @jonas could help you.


Hi @moneta @jonas ,

sorry to ping this again but i am planning to hand in my thesis next week and it would be great if I could cite a reference which explicitly contains this information for the currently used default inter and extrapolation settings.



You can cite the histfactory note for the method. For the default settings, you can look at the code and the code documentation, see ROOT: PiecewiseInterpolation Class Reference



Hi Lorenzo,

thanks for the quick reply and the link.

I guess one of the ideas i had is supported, namely that the exponential extrapolation for normalization uncertainties are combined as a product, while the linearly extrapolated shape effects are summed.

Do you know where in the code i could check what the order of these is? My assumption is that the sum happens first and then the product.


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