pyhf.infer.intervals.upper_limits.upper_limit

pyhf.infer.intervals.upper_limits.upper_limit(data, model, scan=None, level=0.05, return_results=False, **hypotest_kwargs)

Calculate an upper limit interval (0, poi_up) for a single Parameter of Interest (POI) using root-finding or a linear scan through POI-space.

Example

>>> import numpy as np
>>> import pyhf
>>> pyhf.set_backend("numpy")
>>> model = pyhf.simplemodels.uncorrelated_background(
...     signal=[12.0, 11.0], bkg=[50.0, 52.0], bkg_uncertainty=[3.0, 7.0]
... )
>>> observations = [51, 48]
>>> data = pyhf.tensorlib.astensor(observations + model.config.auxdata)
>>> scan = np.linspace(0, 5, 21)
>>> obs_limit, exp_limits, (scan, results) = pyhf.infer.intervals.upper_limits.upper_limit(
...     data, model, scan, return_results=True
... )
>>> np.isclose(obs_limit, 1.01764089)
np.True_
>>> np.isclose(exp_limits, [0.59576921, 0.76169166, 1.08504773, 1.50170482, 2.06654952])
array([ True,  True,  True,  True,  True])

Parameters:

• data (tensor) – The observed data.

• model (Model) – The statistical model adhering to the schema model.json.

• scan (iterable or None) – Iterable of POI values or None to use toms748_scan.

• level (float) – The threshold value to evaluate the interpolated results at.

• return_results (bool) – Whether to return the per-point results.

Returns:

• Tensor: The observed upper limit on the POI.

• Tensor: The expected upper limits on the POI.

• Tuple of Tensors: The given scan along with the hypotest results at each test POI. Only returned when return_results is True.

Return type:

Tuple of Tensors

Added in version 0.7.0.