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=np.ones_like(n_off),
n_off=n_off,
alpha=dataset.alpha.data)
excess_counts =stat.excess_matching_significance(self.sigma)
is_gamma_limited = excess_counts < self.gamma_min
excess_counts[is_gamma_limited] = self.gamma_min
excess = dataset.background.copy()
excess.data = excess_counts
return excess
def calculate_sensitivity_lima(n_on_events, n_background, alpha, n_bins_energy,
n_bins_gammaness, n_bins_theta2):
"""
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, gammaness 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_gammaness: `int` number of bins in gammaness
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_on_events,
n_off=n_background,
alpha=alpha)
n_excesses_5sigma = stat.excess_matching_significance(5)
for i in range(0, n_bins_energy):
for j in range(0, n_bins_gammaness):
for k in range(0, n_bins_theta2):
if n_excesses_5sigma[i][j][k] < 10:
n_excesses_5sigma[i][j][k] = 10
if n_excesses_5sigma[i, j,
k] < 0.05 * n_background[i][j][k] / 5:
n_excesses_5sigma[i, j,
k] = 0.05 * n_background[i][j][k] / 5
sensitivity = n_excesses_5sigma / n_on_events * 100 # percentage of Crab
return n_excesses_5sigma, sensitivity
def calculate_sensitivity_lima_ebin(n_excesses, 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_excesses: `numpy.ndarray` number of excess 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
"""
if any(len(a) != n_bins_energy for a in (n_excesses, n_background, alpha)):
raise ValueError(
'Excess, background and alpha arrays must have the same length')
stat = WStatCountsStatistic(
n_on=np.ones_like(n_background),
n_off=n_background,
alpha=alpha)
n_excesses_5sigma = stat.excess_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_excesses * 100 # percentage of Crab
return n_excesses_5sigma, sensitivity
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.excess_matching_significance(self.n_sigma)
is_gamma_limited = excess_counts < self.gamma_min
excess_counts[is_gamma_limited] = self.gamma_min
excess = Map.from_geom(geom=dataset._geom, data=excess_counts)
return excess
def test_wstat_excess_matching_significance(n_off, alpha, significance,
result):
stat = WStatCountsStatistic(1, n_off, alpha)
excess = stat.excess_matching_significance(significance)
assert_allclose(excess, result, atol=1e-3)
