, pdf, init_pars=None, par_bounds=None, fixed_params=None, **kwargs)[source]

Run a maximum likelihood fit. This is done by minimizing the objective function twice_nll() of the model parameters given the observed data. This is used to produce the maximal likelihood \(L\left(\hat{\mu}, \hat{\boldsymbol{\theta}}\right)\) in the profile likelihood ratio in Equation (7) in [1007.1727]

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


twice_nll() is the objective function given to the optimizer and is returned evaluated at the best fit model parameters when the optional kwarg return_fitted_val is True.


>>> 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)
>>> bestfit_pars, twice_nll =, model, return_fitted_val=True)
>>> bestfit_pars
array([0.        , 1.0030512 , 0.96266961])
>>> twice_nll
>>> -2 * model.logpdf(bestfit_pars, data) == twice_nll
array([ True])
  • data (tensor) – The data

  • 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.

  • kwargs – Keyword arguments passed through to the optimizer API


See optimizer API