Doing a Background only fit

[ssaha1234]

Dear pyhf developers/users,
I have an input json file, with both signal and background values, and I would like to perform two fits on it, one is background only, the other is signal + background fit. I am doing an mle fit as shown in this gist - https://gist.github.com/ssaha1234/0f49934a0806a85a261d7e61e97e8a53

I am trying to understand how to differentiate between bkg only vs signal+ bkg fits, given I have one input json ? I am guessing the above fit result is for signal + bkg fit.
Thank you for the help !

Best,
Shreya

[kratsg]

I have an input json file, with both signal and background values, and I would like to perform two fits on it, one is background only, the other is signal + background fit. I am doing an mle fit as shown in this gist - https://gist.github.com/ssaha1234/0f49934a0806a85a261d7e61e97e8a53

Typically, there's two different kinds of fits one wants to do. One is an MLE fit (unconstrained) and the other is a POI-constrained fit. Usually when someone wants to do an MLE fit for two different models, the way it works is to do something like

# ...
model = ws.model()

# bkg-only fit
pars_bonly = pyhf.infer.mle.fixed_poi_fit(0.0, ws.data(model), model)

# sig+bkg fit
pars_sigpbkg = pyhf.infer.mle.fixed_poi_fit(1.0, ws.data(model), model)

and you compare the fitted parameters, e.g. to compute something like

model.logpdf(pars_bonly)

# vs

model.logpdf(pars_sigpbkg)

Does this clarify?

[alexander-held]

It's a detail, but in a fit with signal + background I would usually expect the signal normalization to free-float, i.e. pyhf.infer.mle.fit instead of fixed_poi_fit. There are certainly places where a fit with POI=1 fixed is desired as well though.

[ssaha1234]

Hi @kratsg and @alexander-held,
Thank you very much for the explanations. If I understand correctly, the POI constrained fit is a background-only fit fixed_poi_fit, and the unconstrained fit, pyhf.infer.mle.fit is for signal+ background.
Best,
Shreya

[alexander-held]

The first example with fixed_poi_fit is a normal background-only fit, yes. You are however free to set the parameters that you hold fixed to any value you like in principle, so it does not have to be a background-only model. The second example in the comment is a fit where the signal normalization is fixed to 1, so there is signal in the model, but it is not allowed to float. pyhf.infer.mle.fit is unconstrained by default. You can customize that further by holding arbitrary parameters fixed at arbitrary values via the respective keyword arguments. That also allows you to reproduce the functionality of fixed_poi_fit via fit. If you look at the source code, the former is really just a convenience function to have a shortcut to achieve this specific case of setting the POI to some value, as that is quite common:

pyhf/src/pyhf/infer/mle.py

Lines 199 to 202 in 9fd99be

	init_pars[pdf.config.poi_index] = poi_val
	fixed_params[pdf.config.poi_index] = True
	return fit(data, pdf, init_pars, par_bounds, fixed_params, **kwargs)

[ssaha1234]

Thanks a lot @alexander-held for the clarification and the code snippets, it is very clear now !
Best,
Shreya