from .. import get_backend
from .utils import loglambdav
[docs]def qmu(mu, data, pdf, init_pars, par_bounds):
r"""
The test statistic, :math:`q_{\mu}`, for establishing an upper
limit on the strength parameter, :math:`\mu`, as defiend in
Equation (14) in :xref:`arXiv:1007.1727`.
.. math::
:nowrap:
\begin{equation}
q_{\mu} = \left\{\begin{array}{ll}
-2\ln\lambda\left(\mu\right), &\hat{\mu} < \mu,\\
0, & \hat{\mu} > \mu
\end{array}\right.
\end{equation}
Args:
mu (Number or Tensor): The signal strength parameter
data (Tensor): The data to be considered
pdf (~pyhf.pdf.Model): The HistFactory statistical model used in the likelihood ratio calculation
init_pars (Tensor): The initial parameters
par_bounds(Tensor): The bounds on the paramter values
Returns:
Float: The calculated test statistic, :math:`q_{\mu}`
"""
tensorlib, optimizer = get_backend()
mubhathat = optimizer.constrained_bestfit(
loglambdav, mu, data, pdf, init_pars, par_bounds
)
muhatbhat = optimizer.unconstrained_bestfit(
loglambdav, data, pdf, init_pars, par_bounds
)
qmu = loglambdav(mubhathat, data, pdf) - loglambdav(muhatbhat, data, pdf)
qmu = tensorlib.where(
muhatbhat[pdf.config.poi_index] > mu, tensorlib.astensor([0]), qmu
)
return qmu