nll scan of POI and nuisance parameters

[diptaparna]

Can you please tell me how to obtain the plot of nll as a function of model parameters (POI and nuisance parameters)?
The x-axis of the plot will be a scan of the parameter values, and the y-axis will be the negative log likelihood for a particular value. I want to make such plot for POI and each of the nuisance parameters separately.

[alexander-held]

Hi @diptaparna, you can get (twice the) NLL returned from a fit via the return_fitted_val keyword argument in pyhf.infer.mle.fit. Performing a scan means setting the parameter over which you are scanning to constant (via the fixed_params argument) and to the specific value you are interested in for the scan (via the init_pars argument). You then repeat that procedure for various parameter values and can then plot the NLL vs the values at which you held the respective parameter fixed.

cabinetry provides you an API for (currently only one-dimensional) likelihood scans: cabinetry.fit.scan, which returns you an object that you can feed to cabinetry.visualize.scan for visualization purposes. A minimal example is below:

import pyhf
import cabinetry

model = pyhf.simplemodels.correlated_background(
    signal=[12.0, 11.0],
    bkg=[50.0, 52.0],
    bkg_up=[45.0, 57.0],
    bkg_down=[55.0, 47.0],
)
data = [67, 58] + model.config.auxdata

scan_results = cabinetry.fit.scan(model, data, "mu")
cabinetry.visualize.scan(scan_results)

which will create the figure figures/scan_mu.pdf. You have to specify the parameter over which you want to scan ("mu" in this case), and you can optionally also specify the parameter range (see the documentation).

You can find the current cabinetry implementation for likelihood scans here: cabinetry/fit/__init__.py#L540-L637. An example of a setup for a 2d likelihood scan is in this gist.