Hello World, pyhf style

Two bin counting experiment with a background uncertainty

import pyhf

Returning the observed and expected \(\mathrm{CL}_{s}\)

pdf = pyhf.simplemodels.hepdata_like(signal_data=[12.0, 11.0], bkg_data=[50.0, 52.0], bkg_uncerts=[3.0, 7.0])
CLs_obs, CLs_exp = pyhf.infer.hypotest(1.0, [51, 48] + pdf.config.auxdata, pdf, return_expected=True)
print('Observed: {}, Expected: {}'.format(CLs_obs, CLs_exp))

Observed: 0.05290116224852556, Expected: 0.06445521290832805

Returning the observed \(\mathrm{CL}_{s}\), \(\mathrm{CL}_{s+b}\), and \(\mathrm{CL}_{b}\)

CLs_obs, p_values = pyhf.infer.hypotest(1.0, [51, 48] + pdf.config.auxdata, pdf, return_tail_probs=True)
print('Observed CL_s: {}, CL_sb: {}, CL_b: {}'.format(CLs_obs, p_values[0], p_values[1]))

Observed CL_s: 0.05290116224852556, CL_sb: 0.023599998519978738, CL_b: 0.4461149342826869

A reminder that

\[\mathrm{CL}_{s} = \frac{\mathrm{CL}_{s+b}}{\mathrm{CL}_{b}} = \frac{p_{s+b}}{1-p_{b}}\]

assert CLs_obs == p_values[0]/p_values[1]

Returning the expected \(\mathrm{CL}_{s}\) band values

import numpy as np

CLs_obs, CLs_exp_band = pyhf.infer.hypotest(1.0, [51, 48] + pdf.config.auxdata, pdf, return_expected_set=True)
print('Observed CL_s: {}\n'.format(CLs_obs))
for p_value, n_sigma in enumerate(np.arange(-2,3)):
    print('Expected CL_s{}: {}'.format('      ' if n_sigma==0 else '({} σ)'.format(n_sigma),CLs_exp_band[p_value]))

Observed CL_s: 0.05290116224852556

Expected CL_s(-2 σ): 0.0026064088679947964
Expected CL_s(-1 σ): 0.013820657528619273
Expected CL_s      : 0.06445521290832805
Expected CL_s(1 σ): 0.23526103626937836
Expected CL_s(2 σ): 0.5730418174887743