from scipy import interpolate
from .basetest import BaseTest
from ..exceptions import POIRangeError
[docs]class ConfidenceInterval(BaseTest):
"""Class for confidence interval calculation.
Args:
* **calculator** (`sktats.hypotests.BaseCalculator`): calculator to use for computing the pvalues
* **poinull** (`POIarray`): parameters of interest for the null hypothesis
* **qtilde** (bool, optional): if `True` use the :math:`\widetilde{q}` test statistics else (default) use the :math:`q` test statistic
Example with `zfit`:
>>> import numpy as np
>>> import zfit
>>> from zfit.loss import ExtendedUnbinnedNLL
>>> from zfit.minimize import Minuit
>>> bounds = (0.1, 3.0)
>>> zfit.Space('x', limits=bounds)
>>> bkg = np.random.exponential(0.5, 300)
>>> peak = np.random.normal(1.2, 0.1, 80)
>>> data = np.concatenate((bkg, peak))
>>> data = data[(data > bounds[0]) & (data < bounds[1])]
>>> N = data.size
>>> data = zfit.data.Data.from_numpy(obs=obs, array=data)
>>> mean = zfit.Parameter("mean", 1.2, 0.5, 2.0)
>>> sigma = zfit.Parameter("sigma", 0.1, 0.02, 0.2)
>>> lambda_ = zfit.Parameter("lambda", -2.0, -4.0, -1.0)
>>> Nsig = zfit.Parameter("Ns", 20., -20., N)
>>> Nbkg = zfit.Parameter("Nbkg", N, 0., N*1.1)
>>> signal = Nsig * zfit.pdf.Gauss(obs=obs, mu=mean, sigma=sigma)
>>> background = Nbkg * zfit.pdf.Exponential(obs=obs, lambda_=lambda_)
>>> loss = ExtendedUnbinnedNLL(model=signal + background, data=data)
>>> from hepstats.hypotests.calculators import AsymptoticCalculator
>>> from hepstats.hypotests import ConfidenceInterval
>>> from hepstats.hypotests.parameters import POI, POIarray
>>> calculator = AsymptoticCalculator(loss, Minuit())
>>> poinull = POIarray(mean, np.linspace(1.15, 1.26, 100))
>>> ci = ConfidenceInterval(calculator, poinull)
>>> ci.interval()
Confidence interval on mean:
1.1810371356602791 < mean < 1.2156701172321935 at 68.0% C.L.
"""
def __init__(self, calculator, poinull, qtilde=False):
super(ConfidenceInterval, self).__init__(calculator, poinull)
self._qtilde = qtilde
@property
def qtilde(self):
"""
Returns True if qtilde test statistic is used, else False.
"""
return self._qtilde
[docs] def pvalues(self):
"""
Returns p-values scanned for the values of the parameters of interest
in the null hypothesis.
Returns:
pvalues (`np.array`): CLsb, CLs, expected (+/- sigma bands) p-values
"""
return self.calculator.pvalue(self.poinull, qtilde=self.qtilde, onesided=False)[0]
[docs] def interval(self, alpha=0.32, printlevel=1):
"""
Returns the confidence level on the parameter of interest.
Args:
* **alpha** (float, default=0.32/1 sigma): significance level,
* **printlevel** (int, default=1): if > 0 print the result
Returns:
limits (Dict): central, upper and lower bounds on the parameter of interest
"""
poinull = self.poinull
observed = self.calculator.bestfit.params[poinull.parameter]["value"]
if min(self.pvalues()) > alpha:
msg = f"The minimum of the scanned p-values is {min(self.pvalues())} which is larger than the"
msg += f" confidence level alpha = {alpha}. Try to increase the range of POI values."
raise POIRangeError(msg)
tck = interpolate.splrep(poinull.values, self.pvalues() - alpha, s=0)
root = interpolate.sproot(tck)
bands = {}
bands["observed"] = observed
if len(root) < 2:
msg = f" bound on the POI `{poinull.name}` cannot not be interpolated."
if root[0] < observed:
msg = "Upper" + msg + " Try to increase the maximum POI value."
else:
msg = "Low" + msg + " Try to decrease the minimum POI value."
raise POIRangeError(msg)
else:
bands["lower"] = root[0]
bands["upper"] = root[1]
if printlevel > 0:
msg = f"\nConfidence interval on {poinull.name}:\n"
msg += f"\t{root[0]} < {poinull.name} < {root[1]} at {(1-alpha)*100:.1f}% C.L."
print(msg)
return bands