pyhf.infer.test_statistics.tmu¶

pyhf.infer.test_statistics.tmu(mu, data, pdf, init_pars, par_bounds)[source]¶

The test statistic, \(t_{\mu}\), for establishing a two-sided interval on the strength parameter, \(\mu\), as defiend in Equation (10) in [1007.1727].

Example

>>> import pyhf
>>> pyhf.set_backend("numpy")
>>> model = pyhf.simplemodels.hepdata_like(
...     signal_data=[12.0, 11.0], bkg_data=[50.0, 52.0], bkg_uncerts=[3.0, 7.0]
... )
>>> observations = [51, 48]
>>> data = pyhf.tensorlib.astensor(observations + model.config.auxdata)
>>> test_mu = 1.0
>>> init_pars = model.config.suggested_init()
>>> par_bounds = model.config.suggested_bounds()
>>> par_bounds[model.config.poi_index] = [-10.0, 10.0]
>>> pyhf.infer.test_statistics.tmu(test_mu, data, model, init_pars, par_bounds)
array(3.9549891)

Parameters

mu (Number or Tensor) – The signal strength parameter
data (Tensor) – The data to be considered
pdf (Model) – The statistical model adhering to the schema model.json
init_pars (list) – Values to initialize the model parameters at for the fit
par_bounds (list of lists or tuples) – The extrema of values the model parameters are allowed to reach in the fit

Returns

The calculated test statistic, \(t_{\mu}\)

Return type

Float