Source code for pyhf.infer.test_statistics

from pyhf import get_backend
from pyhf.infer.mle import fixed_poi_fit, fit
from pyhf.exceptions import UnspecifiedPOI

import logging

log = logging.getLogger(__name__)

__all__ = ["q0", "qmu", "qmu_tilde", "tmu", "tmu_tilde"]


def __dir__():
    return __all__


def _qmu_like(
    mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_pars=False
):
    """
    Clipped version of _tmu_like where the returned test statistic
    is 0 if muhat > 0 else tmu_like_stat.

    If the lower bound of the POI is 0 this automatically implements
    qmu_tilde. Otherwise this is qmu (no tilde).
    """
    tensorlib, optimizer = get_backend()
    tmu_like_stat, (mubhathat, muhatbhat) = _tmu_like(
        mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_pars=True
    )
    qmu_like_stat = tensorlib.where(
        muhatbhat[pdf.config.poi_index] > mu, tensorlib.astensor(0.0), tmu_like_stat
    )
    if return_fitted_pars:
        return qmu_like_stat, (mubhathat, muhatbhat)
    return qmu_like_stat


def _tmu_like(
    mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_pars=False
):
    """
    Basic Profile Likelihood test statistic.

    If the lower bound of the POI is 0 this automatically implements
    tmu_tilde. Otherwise this is tmu (no tilde).
    """
    tensorlib, optimizer = get_backend()
    mubhathat, fixed_poi_fit_lhood_val = fixed_poi_fit(
        mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_val=True
    )
    muhatbhat, unconstrained_fit_lhood_val = fit(
        data, pdf, init_pars, par_bounds, fixed_params, return_fitted_val=True
    )
    log_likelihood_ratio = fixed_poi_fit_lhood_val - unconstrained_fit_lhood_val
    tmu_like_stat = tensorlib.astensor(
        tensorlib.clip(log_likelihood_ratio, 0.0, max_value=None)
    )
    if return_fitted_pars:
        return tmu_like_stat, (mubhathat, muhatbhat)
    return tmu_like_stat


[docs] def qmu(mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_pars=False): r""" The test statistic, :math:`q_{\mu}`, for establishing an upper limit on the strength parameter, :math:`\mu`, as defined 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} \leq \mu,\\ 0, & \hat{\mu} > \mu \end{array}\right. \end{equation} where :math:`\lambda\left(\mu\right)` is the profile likelihood ratio as defined in Equation (7) .. math:: \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.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) >>> 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.qmu( ... test_mu, data, model, init_pars, par_bounds, fixed_params ... ) array(3.9549891) >>> pyhf.infer.test_statistics.qmu( ... test_mu, data, model, init_pars, par_bounds, fixed_params, return_fitted_pars=True ... ) (array(3.9549891), (array([1. , 0.97224597, 0.87553894]), array([-0.06679525, 1.00555369, 0.96930896]))) 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 (:obj:`list` of :obj:`float`): The starting values of the model parameters for minimization. par_bounds (:obj:`list` of :obj:`list`/:obj:`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 (:obj:`list` of :obj:`bool`): The flag to set a parameter constant to its starting value during minimization. return_fitted_pars (:obj:`bool`): Return the best-fit parameter tensors the fixed-POI and unconstrained fits have converged on (i.e. :math:`\mu, \hat{\hat{\theta}}` and :math:`\hat{\mu}, \hat{\theta}`) Returns: Tuple of a Float and a Tuple of Tensors: - The calculated test statistic, :math:`q_{\mu}` - The parameter tensors corresponding to the constrained and unconstrained best fit, :math:`\mu, \hat{\hat{\theta}}` and :math:`\hat{\mu}, \hat{\theta}`. Only returned if ``return_fitted_pars`` is ``True``. """ if pdf.config.poi_index is None: raise UnspecifiedPOI( 'No POI is defined. A POI is required for profile likelihood based test statistics.' ) if par_bounds[pdf.config.poi_index][0] == 0: log.warning( 'qmu test statistic used for fit configuration with POI bounded at zero.\n' + 'Use the qmu_tilde test statistic (pyhf.infer.test_statistics.qmu_tilde) instead.' ) return _qmu_like( mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_pars=return_fitted_pars, )
[docs] def qmu_tilde( mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_pars=False ): r""" The "alternative" test statistic, :math:`\tilde{q}_{\mu}`, for establishing an upper limit on the strength parameter, :math:`\mu`, for models with bounded POI, as defined in Equation (16) in :xref:`arXiv:1007.1727` .. math:: :nowrap: \begin{equation} \tilde{q}_{\mu} = \left\{\begin{array}{ll} -2\ln\tilde{\lambda}\left(\mu\right), &\hat{\mu} \leq \mu,\\ 0, & \hat{\mu} > \mu \end{array}\right. \end{equation} where :math:`\tilde{\lambda}\left(\mu\right)` is the constrained profile likelihood ratio as defined in Equation (10) .. math:: :nowrap: \begin{equation} \tilde{\lambda}\left(\mu\right) = \left\{\begin{array}{ll} \frac{L\left(\mu, \hat{\hat{\boldsymbol{\theta}}}(\mu)\right)}{L\left(\hat{\mu}, \hat{\hat{\boldsymbol{\theta}}}(0)\right)}, &\hat{\mu} < 0,\\ \frac{L\left(\mu, \hat{\hat{\boldsymbol{\theta}}}(\mu)\right)}{L\left(\hat{\mu}, \hat{\boldsymbol{\theta}}\right)}, &\hat{\mu} \geq 0. \end{array}\right. \end{equation} 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) >>> test_mu = 1.0 >>> init_pars = model.config.suggested_init() >>> par_bounds = model.config.suggested_bounds() >>> fixed_params = model.config.suggested_fixed() >>> pyhf.infer.test_statistics.qmu_tilde( ... test_mu, data, model, init_pars, par_bounds, fixed_params ... ) array(3.93824492) >>> pyhf.infer.test_statistics.qmu_tilde( ... test_mu, data, model, init_pars, par_bounds, fixed_params, return_fitted_pars=True ... ) (array(3.93824492), (array([1. , 0.97224597, 0.87553894]), array([0. , 1.0030512 , 0.96266961]))) Args: mu (Number or Tensor): The signal strength parameter data (:obj:`tensor`): The data to be considered pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json init_pars (:obj:`list` of :obj:`float`): The starting values of the model parameters for minimization. par_bounds (:obj:`list` of :obj:`list`/:obj:`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 (:obj:`list` of :obj:`bool`): The flag to set a parameter constant to its starting value during minimization. return_fitted_pars (:obj:`bool`): Return the best-fit parameter tensors the fixed-POI and unconstrained fits have converged on (i.e. :math:`\mu, \hat{\hat{\theta}}` and :math:`\hat{\mu}, \hat{\theta}`) Returns: Tuple of a Float and a Tuple of Tensors: - The calculated test statistic, :math:`\tilde{q}_{\mu}` - The parameter tensors corresponding to the constrained best fit, :math:`\mu, \hat{\hat{\theta}}`, and the unconstrained best fit, :math:`\hat{\mu}, \hat{\theta}`. Only returned if ``return_fitted_pars`` is ``True``. """ if pdf.config.poi_index is None: raise UnspecifiedPOI( 'No POI is defined. A POI is required for profile likelihood based test statistics.' ) if par_bounds[pdf.config.poi_index][0] != 0: log.warning( 'qmu_tilde test statistic used for fit configuration with POI not bounded at zero.\n' + 'Use the qmu test statistic (pyhf.infer.test_statistics.qmu) instead.' ) return _qmu_like( mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_pars=return_fitted_pars, )
[docs] def tmu(mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_pars=False): r""" The test statistic, :math:`t_{\mu}`, for establishing a two-sided interval on the strength parameter, :math:`\mu`, as defined in Equation (8) in :xref:`arXiv:1007.1727` .. math:: t_{\mu} = -2\ln\lambda\left(\mu\right) where :math:`\lambda\left(\mu\right)` is the profile likelihood ratio as defined in Equation (7) .. math:: \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.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) >>> 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) >>> pyhf.infer.test_statistics.tmu( ... test_mu, data, model, init_pars, par_bounds, fixed_params, return_fitted_pars=True ... ) (array(3.9549891), (array([1. , 0.97224597, 0.87553894]), array([-0.06679525, 1.00555369, 0.96930896]))) Args: mu (Number or Tensor): The signal strength parameter data (Tensor): The data to be considered pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json init_pars (:obj:`list` of :obj:`float`): The starting values of the model parameters for minimization. par_bounds (:obj:`list` of :obj:`list`/:obj:`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 (:obj:`list` of :obj:`bool`): The flag to set a parameter constant to its starting value during minimization. return_fitted_pars (:obj:`bool`): Return the best-fit parameter tensors the fixed-POI and unconstrained fits have converged on (i.e. :math:`\mu, \hat{\hat{\theta}}` and :math:`\hat{\mu}, \hat{\theta}`) Returns: Tuple of a Float and a Tuple of Tensors: - The calculated test statistic, :math:`t_{\mu}` - The parameter tensors corresponding to the constrained best fit, :math:`\mu, \hat{\hat{\theta}}`, and the unconstrained best fit, :math:`\hat{\mu}, \hat{\theta}`. Only returned if ``return_fitted_pars`` is ``True``. """ if pdf.config.poi_index is None: raise UnspecifiedPOI( 'No POI is defined. A POI is required for profile likelihood based test statistics.' ) if par_bounds[pdf.config.poi_index][0] == 0: log.warning( 'tmu test statistic used for fit configuration with POI bounded at zero.\n' + 'Use the tmu_tilde test statistic (pyhf.infer.test_statistics.tmu_tilde) instead.' ) return _tmu_like( mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_pars=return_fitted_pars, )
[docs] def tmu_tilde( mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_pars=False ): r""" The test statistic, :math:`\tilde{t}_{\mu}`, for establishing a two-sided interval on the strength parameter, :math:`\mu`, for models with bounded POI, as defined in Equation (11) in :xref:`arXiv:1007.1727` .. math:: \tilde{t}_{\mu} = -2\ln\tilde{\lambda}\left(\mu\right) where :math:`\tilde{\lambda}\left(\mu\right)` is the constrained profile likelihood ratio as defined in Equation (10) .. math:: :nowrap: \begin{equation} \tilde{\lambda}\left(\mu\right) = \left\{\begin{array}{ll} \frac{L\left(\mu, \hat{\hat{\boldsymbol{\theta}}}(\mu)\right)}{L\left(\hat{\mu}, \hat{\hat{\boldsymbol{\theta}}}(0)\right)}, &\hat{\mu} < 0,\\ \frac{L\left(\mu, \hat{\hat{\boldsymbol{\theta}}}(\mu)\right)}{L\left(\hat{\mu}, \hat{\boldsymbol{\theta}}\right)}, &\hat{\mu} \geq 0. \end{array}\right. \end{equation} 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) >>> test_mu = 1.0 >>> init_pars = model.config.suggested_init() >>> par_bounds = model.config.suggested_bounds() >>> fixed_params = model.config.suggested_fixed() >>> pyhf.infer.test_statistics.tmu_tilde( ... test_mu, data, model, init_pars, par_bounds, fixed_params ... ) array(3.93824492) >>> pyhf.infer.test_statistics.tmu_tilde( ... test_mu, data, model, init_pars, par_bounds, fixed_params, return_fitted_pars=True ... ) (array(3.93824492), (array([1. , 0.97224597, 0.87553894]), array([0. , 1.0030512 , 0.96266961]))) Args: mu (Number or Tensor): The signal strength parameter data (:obj:`tensor`): The data to be considered pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json init_pars (:obj:`list` of :obj:`float`): The starting values of the model parameters for minimization. par_bounds (:obj:`list` of :obj:`list`/:obj:`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 (:obj:`list` of :obj:`bool`): The flag to set a parameter constant to its starting value during minimization. return_fitted_pars (:obj:`bool`): Return the best-fit parameter tensors the fixed-POI and unconstrained fits have converged on (i.e. :math:`\mu, \hat{\hat{\theta}}` and :math:`\hat{\mu}, \hat{\theta}`) Returns: Tuple of a Float and a Tuple of Tensors: - The calculated test statistic, :math:`\tilde{t}_{\mu}` - The parameter tensors corresponding to the constrained best fit, :math:`\mu, \hat{\hat{\theta}}`, and the unconstrained best fit, :math:`\hat{\mu}, \hat{\theta}`. Only returned if ``return_fitted_pars`` is ``True``. """ if pdf.config.poi_index is None: raise UnspecifiedPOI( 'No POI is defined. A POI is required for profile likelihood based test statistics.' ) if par_bounds[pdf.config.poi_index][0] != 0: log.warning( 'tmu_tilde test statistic used for fit configuration with POI not bounded at zero.\n' + 'Use the tmu test statistic (pyhf.infer.test_statistics.tmu) instead.' ) return _tmu_like( mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_pars=return_fitted_pars, )
[docs] def q0(mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_pars=False): r""" The test statistic, :math:`q_{0}`, for discovery of a positive signal as defined in Equation (12) in :xref:`arXiv:1007.1727`, for :math:`\mu=0`. .. math:: :nowrap: \begin{equation} q_{0} = \left\{\begin{array}{ll} -2\ln\lambda\left(0\right), &\hat{\mu} \ge 0,\\ 0, & \hat{\mu} < 0, \end{array}\right. \end{equation} 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 = [60, 65] >>> data = pyhf.tensorlib.astensor(observations + model.config.auxdata) >>> test_mu = 0.0 >>> init_pars = model.config.suggested_init() >>> par_bounds = model.config.suggested_bounds() >>> fixed_params = model.config.suggested_fixed() >>> pyhf.infer.test_statistics.q0(test_mu, data, model, init_pars, par_bounds, fixed_params) array(2.98339447) >>> pyhf.infer.test_statistics.q0( ... test_mu, data, model, init_pars, par_bounds, fixed_params, return_fitted_pars=True ... ) (array(2.98339447), (array([0. , 1.03050845, 1.12128752]), array([0.95260667, 0.99635345, 1.02140172]))) Args: mu (Number or Tensor): The signal strength parameter (must be set to zero) data (Tensor): The data to be considered pdf (~pyhf.pdf.Model): The HistFactory statistical model used in the likelihood ratio calculation init_pars (:obj:`list` of :obj:`float`): The starting values of the model parameters for minimization. par_bounds (:obj:`list` of :obj:`list`/:obj:`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 (:obj:`list` of :obj:`bool`): The flag to set a parameter constant to its starting value during minimization. return_fitted_pars (:obj:`bool`): Return the best-fit parameter tensors the fixed-POI and unconstrained fits have converged on (i.e. :math:`\mu, \hat{\hat{\theta}}` and :math:`\hat{\mu}, \hat{\theta}`) Returns: Tuple of a Float and a Tuple of Tensors: - The calculated test statistic, :math:`q_{0}` - The parameter tensors corresponding to the constrained best fit, :math:`\mu, \hat{\hat{\theta}}`, and the unconstrained best fit, :math:`\hat{\mu}, \hat{\theta}`. Only returned if ``return_fitted_pars`` is ``True``. """ if pdf.config.poi_index is None: raise UnspecifiedPOI( 'No POI is defined. A POI is required for profile likelihood based test statistics.' ) if mu != 0.0: log.warning( 'q0 test statistic only used for fit configuration with POI set to zero. Setting mu=0.' ) mu = 0.0 tensorlib, optimizer = get_backend() tmu_like_stat, (mubhathat, muhatbhat) = _tmu_like( mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_pars=True ) q0_stat = tensorlib.where( muhatbhat[pdf.config.poi_index] < 0, tensorlib.astensor(0.0), tmu_like_stat ) if return_fitted_pars: return q0_stat, (mubhathat, muhatbhat) return q0_stat