pyhf.infer.mle.twice_nll#

pyhf.infer.mle.twice_nll(pars, data, pdf)[source]#

Two times the negative log-likelihood of the model parameters, $(\mu ,\mathit{\theta })$, given the observed data. It is used in the calculation of the test statistic, $t_{\mu }$, as defined 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)

$$\lambda \left(\mu \right)=\frac{L(\mu ,\widehat{\hat{\mathit{\theta }}})}{L(\hat{\mu },\hat{\mathit{\theta }})}.$$

It serves as the objective function to minimize in fit() and fixed_poi_fit().

Example

>>> 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)
>>> parameters = model.config.suggested_init()  # nominal parameters
>>> twice_nll = pyhf.infer.mle.twice_nll(parameters, data, model)
>>> twice_nll
array([30.77525435])
>>> -2 * model.logpdf(parameters, data) == twice_nll
array([ True])

Parameters:

• pars (tensor) – The parameters of the HistFactory model

• data (tensor) – The data to be considered

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

Returns:

Two times the negative log-likelihood, $-2\ln L(\mu ,\mathit{\theta })$

Return type:

Tensor