pyhf.infer.test_statistics.tmu

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

The test statistic, \(t_{\mu}\), for establishing a two-sided interval on the strength parameter, \(\mu\), as defiend in Equation (8) in [1007.1727]

\[t_{\mu} = -2\ln\lambda\left(\mu\right)\]

where \(\lambda\left(\mu\right)\) is the profile likelihood ratio as defined in Equation (7)

\[\lambda\left(\mu\right) = \frac{L\left(\mu, \hat{\hat{\boldsymbol{\theta}}}\right)}{L\left(\hat{\mu}, \hat{\boldsymbol{\theta}}\right)}\,.\]

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]
>>> fixed_params = model.config.suggested_fixed()
>>> pyhf.infer.test_statistics.tmu(test_mu, data, model, init_pars, par_bounds, fixed_params)
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 of float) – The starting values of the model parameters for minimization.

  • par_bounds (list of list/tuple) – The extrema of values the model parameters are allowed to reach in the fit. The shape should be (n, 2) for n model parameters.

  • fixed_params (list of bool) – The flag to set a parameter constant to its starting value during minimization.

Returns

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

Return type

Float