# Hello World, pyhf style#

Two bin counting experiment with a background uncertainty

[1]:

import pyhf


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

[2]:

model = pyhf.simplemodels.uncorrelated_background(
signal=[12.0, 11.0], bkg=[50.0, 52.0], bkg_uncertainty=[3.0, 7.0]
)
data = [51, 48] + model.config.auxdata
test_mu = 1.0
CLs_obs, CLs_exp = pyhf.infer.hypotest(
test_mu, data, model, test_stat="qtilde", return_expected=True
)
print(f"Observed: {CLs_obs}, Expected: {CLs_exp}")

Observed: 0.052515541856109765, Expected: 0.06445521290832805


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

[3]:

CLs_obs, p_values = pyhf.infer.hypotest(
test_mu, data, model, test_stat="qtilde", return_tail_probs=True
)
print(f"Observed CL_s: {CLs_obs}, CL_sb: {p_values[0]}, CL_b: {p_values[1]}")

Observed CL_s: 0.052515541856109765, CL_sb: 0.023324961200974572, CL_b: 0.44415349012077077


A reminder that

$\mathrm{CL}_{s} = \frac{\mathrm{CL}_{s+b}}{\mathrm{CL}_{b}} = \frac{p_{s+b}}{1-p_{b}}$
[4]:

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


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

[5]:

import numpy as np

[6]:

CLs_obs, CLs_exp_band = pyhf.infer.hypotest(
test_mu, data, model, test_stat="qtilde", return_expected_set=True
)
print(f"Observed CL_s: {CLs_obs}\n")
for p_value, n_sigma in enumerate(np.arange(-2, 3)):
print(
"Expected CL_s{}: {}".format(
"      " if n_sigma == 0 else f"({n_sigma} σ)",
CLs_exp_band[p_value],
)
)

Observed CL_s: 0.052515541856109765

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