"""Module for Maximum Likelihood Estimation."""
from .. import get_backend
[docs]def twice_nll(pars, data, pdf):
"""
Twice the negative Log-Likelihood.
Args:
data (`tensor`): The data
pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json
Returns:
Twice the negative log likelihood.
"""
return -2 * pdf.logpdf(pars, data)
[docs]def fit(data, pdf, init_pars=None, par_bounds=None, **kwargs):
"""
Run a unconstrained maximum likelihood fit.
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)
>>> pyhf.infer.mle.fit(data, model, return_fitted_val=True)
(array([0. , 1.0030512 , 0.96266961]), array([24.98393521]))
Args:
data (`tensor`): The data
pdf (~pyhf.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 `list`\s or `tuple`\s): The extrema of values the model parameters are allowed to reach in the fit
kwargs: Keyword arguments passed through to the optimizer API
Returns:
See optimizer API
"""
_, opt = get_backend()
init_pars = init_pars or pdf.config.suggested_init()
par_bounds = par_bounds or pdf.config.suggested_bounds()
return opt.minimize(twice_nll, data, pdf, init_pars, par_bounds, **kwargs)
[docs]def fixed_poi_fit(poi_val, data, pdf, init_pars=None, par_bounds=None, **kwargs):
"""
Run a maximum likelihood fit with the POI value fixed.
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_poi = 1.0
>>> pyhf.infer.mle.fixed_poi_fit(test_poi, data, model, return_fitted_val=True)
(array([1. , 0.97224597, 0.87553894]), array([28.92218013]))
Args:
data: The data
pdf (~pyhf.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 `list`\s or `tuple`\s): The extrema of values the model parameters are allowed to reach in the fit
kwargs: Keyword arguments passed through to the optimizer API
Returns:
See optimizer API
"""
_, opt = get_backend()
init_pars = init_pars or pdf.config.suggested_init()
par_bounds = par_bounds or pdf.config.suggested_bounds()
return opt.minimize(
twice_nll,
data,
pdf,
init_pars,
par_bounds,
[(pdf.config.poi_index, poi_val)],
**kwargs,
)