def estimate_min_excess(self, dataset):
"""Estimate minimum excess to reach the given significance.
Parameters
----------
dataset : `SpectrumDataset`
Spectrum dataset
Returns
-------
excess : `RegionNDMap`
Minimal excess
"""
n_off = dataset.counts_off.data
stat = WStatCountsStatistic(
n_on=dataset.alpha.data * n_off, n_off=n_off, alpha=dataset.alpha.data
)
excess_counts = stat.n_sig_matching_significance(self.n_sigma)
is_gamma_limited = excess_counts < self.gamma_min
excess_counts[is_gamma_limited] = self.gamma_min
bkg_syst_limited = (
excess_counts < self.bkg_syst_fraction * dataset.background.data
)
excess_counts[bkg_syst_limited] = (
self.bkg_syst_fraction * dataset.background.data[bkg_syst_limited]
)
excess = Map.from_geom(geom=dataset._geom, data=excess_counts)
return excess
def calculate_sensitivity_lima_ebin(n_on_events, n_background, alpha,
n_bins_energy):
"""
Sensitivity calculation using the Li & Ma formula
eq. 17 of Li & Ma (1983).
https://ui.adsabs.harvard.edu/abs/1983ApJ...272..317L/abstract
Parameters
---------
n_on_events: `numpy.ndarray` number of ON events in the signal region
n_background: `numpy.ndarray` number of events in the background region
alpha: `float` inverse of the number of off positions
n_bins_energy:`int` number of bins in energy
Returns
---------
sensitivity: `numpy.ndarray` sensitivity in percentage of Crab units
n_excesses_5sigma: `numpy.ndarray` number of excesses corresponding to
a 5 sigma significance
"""
stat = WStatCountsStatistic(n_on=n_on_events,
n_off=n_background,
alpha=alpha)
n_excesses_5sigma = stat.n_sig_matching_significance(5)
for i in range(0, n_bins_energy):
# If the excess needed to get 5 sigma is less than 10,
# we force it to be at least 10
if n_excesses_5sigma[i] < 10:
n_excesses_5sigma[i] = 10
# If the excess needed to get 5 sigma is less than 5%
# of the background, we force it to be at least 5% of
# the background
if n_excesses_5sigma[i] < 0.05 * n_background[i] * alpha[i]:
n_excesses_5sigma[i] = 0.05 * n_background[i] * alpha[i]
sensitivity = n_excesses_5sigma / n_on_events * 100 # percentage of Crab
return n_excesses_5sigma, sensitivity
def calculate_sensitivity_lima(n_signal, n_background, alpha):
"""
Sensitivity calculation using the Li & Ma formula
eq. 17 of Li & Ma (1983).
https://ui.adsabs.harvard.edu/abs/1983ApJ...272..317L/abstract
We calculate the sensitivity in bins of energy and
theta2
Parameters
----------
n_on_events: `numpy.ndarray` number of ON events in the signal region
n_background: `numpy.ndarray` number of events in the background region
alpha: `float` inverse of the number of off positions
n_bins_energy: `int` number of bins in energy
n_bins_theta2: `int` number of bins in theta2
Returns
-------
sensitivity: `numpy.ndarray` sensitivity in percentage of Crab units
n_excesses_5sigma: `numpy.ndarray` number of excesses corresponding to
a 5 sigma significance
"""
stat = WStatCountsStatistic(n_on=n_signal + alpha * n_background,
n_off=n_background,
alpha=alpha)
n_excesses_5sigma = stat.n_sig_matching_significance(5)
n_excesses_5sigma[n_excesses_5sigma < 10] = 10
bkg_5percent = 0.05 * n_background * alpha
n_excesses_5sigma[n_excesses_5sigma < bkg_5percent] = bkg_5percent[
n_excesses_5sigma < bkg_5percent]
sensitivity = n_excesses_5sigma / (n_signal) * 100 # percentage of Crab
return n_excesses_5sigma, sensitivity
def test_wstat_excess_matching_significance(n_off, alpha, significance, result):
stat = WStatCountsStatistic(1, n_off, alpha)
excess = stat.n_sig_matching_significance(significance)
assert_allclose(excess, result, rtol=1e-2)
