def calc_wstat_gammapy():
data, model, staterr, off_vec, alpha = get_test_data()
from gammapy.stats import wstat
from gammapy.stats.fit_statistics import (
_get_wstat_background,
_get_wstat_extra_terms,
)
# background estimate
bkg = _get_wstat_background(data, off_vec, alpha, model)
print("Gammapy mu_bkg: {}".format(bkg))
statsvec = wstat(n_on=data, mu_signal=model, n_off=off_vec, alpha=alpha)
print("Gammapy stat: {}".format(np.sum(statsvec)))
print("Gammapy statsvec: {}".format(statsvec))
print("---> with extra terms")
extra_terms = _get_wstat_extra_terms(data, off_vec)
print("Gammapy extra terms: {}".format(extra_terms))
statsvec = wstat(n_on=data,
mu_signal=model,
n_off=off_vec,
alpha=alpha,
extra_terms=True)
print("Gammapy stat: {}".format(np.sum(statsvec)))
print("Gammapy statsvec: {}".format(statsvec))
def calc_wstat_gammapy():
data, model, staterr, off_vec, alpha = get_test_data()
from gammapy.stats import wstat
from gammapy.stats.fit_statistics import (
_get_wstat_background,
_get_wstat_extra_terms,
)
# background estimate
bkg = _get_wstat_background(data, off_vec, alpha, model)
print("Gammapy mu_bkg: {}".format(bkg))
statsvec = wstat(n_on=data,
mu_signal=model,
n_off=off_vec,
alpha=alpha)
print("Gammapy stat: {}".format(np.sum(statsvec)))
print("Gammapy statsvec: {}".format(statsvec))
print("---> with extra terms")
extra_terms = _get_wstat_extra_terms(data, off_vec)
print("Gammapy extra terms: {}".format(extra_terms))
statsvec = wstat(n_on=data,
mu_signal=model,
n_off=off_vec,
alpha=alpha, extra_terms=True)
print("Gammapy stat: {}".format(np.sum(statsvec)))
print("Gammapy statsvec: {}".format(statsvec))
def _excess_matching_significance_fcn(self, excess, significance, index):
TS0 = wstat(excess + self.background[index], self.n_off[index],
self.alpha[index], 0)
TS1 = wstat(excess + self.background[index], self.n_off[index],
self.alpha[index], excess)
return np.sign(excess) * np.sqrt(np.clip(TS0 - TS1, 0,
None)) - significance
def test_wstat_corner_cases():
"""test WSTAT formulae for corner cases"""
n_on = 0
n_off = 5
mu_sig = 2.3
alpha = 0.5
actual = stats.wstat(n_on=n_on, mu_sig=mu_sig, n_off=n_off, alpha=alpha)
desired = 2 * (mu_sig + n_off * np.log(1 + alpha))
assert_allclose(actual, desired)
actual = stats.get_wstat_mu_bkg(n_on=n_on,
mu_sig=mu_sig,
n_off=n_off,
alpha=alpha)
desired = n_off / (alpha + 1)
assert_allclose(actual, desired)
# n_off = 0 and mu_sig < n_on * (alpha / alpha + 1)
n_on = 9
n_off = 0
mu_sig = 2.3
alpha = 0.5
actual = stats.wstat(n_on=n_on, mu_sig=mu_sig, n_off=n_off, alpha=alpha)
desired = -2 * (mu_sig * (1.0 / alpha) + n_on * np.log(alpha /
(1 + alpha)))
assert_allclose(actual, desired)
actual = stats.get_wstat_mu_bkg(n_on=n_on,
mu_sig=mu_sig,
n_off=n_off,
alpha=alpha)
desired = n_on / (1 + alpha) - (mu_sig / alpha)
assert_allclose(actual, desired)
# n_off = 0 and mu_sig > n_on * (alpha / alpha + 1)
n_on = 5
n_off = 0
mu_sig = 5.3
alpha = 0.5
actual = stats.wstat(n_on=n_on, mu_sig=mu_sig, n_off=n_off, alpha=alpha)
desired = 2 * (mu_sig + n_on * (np.log(n_on) - np.log(mu_sig) - 1))
assert_allclose(actual, desired)
actual = stats.get_wstat_mu_bkg(n_on=n_on,
mu_sig=mu_sig,
n_off=n_off,
alpha=alpha)
assert_allclose(actual, 0)
def test_wstat(test_data, reference_values):
statsvec = stats.wstat(
n_on=test_data["n_on"],
mu_sig=test_data["mu_sig"],
n_off=test_data["n_off"],
alpha=test_data["alpha"],
extra_terms=True,
)
assert_allclose(statsvec, reference_values["wstat"])
def stat_array(self):
"""Likelihood per bin given the current model parameters"""
mu_sig = self.npred_sig().data
on_stat_ = wstat(
n_on=self.counts.data,
n_off=self.counts_off.data,
alpha=self.alpha,
mu_sig=mu_sig,
)
return np.nan_to_num(on_stat_)
def likelihood_per_bin(self):
"""Likelihood per bin given the current model parameters"""
mu_sig = self.npred().data
on_stat_ = wstat(
n_on=self.counts.data,
n_off=self.counts_off.data,
alpha=list(self.alpha.data),
mu_sig=mu_sig,
)
return np.nan_to_num(on_stat_)
def calc_wstat_xspec():
data, model, staterr, off_vec, alpha = get_test_data()
from xspec_stats import xspec_wstat as wstat
from xspec_stats import xspec_wstat_f, xspec_wstat_d
# alpha = t_s / t_b
t_b = 1. / alpha
t_s = 1
d = xspec_wstat_d(t_s, t_b, model, data, off_vec)
f = xspec_wstat_f(data, off_vec, t_s, t_b, model, d)
bkg = f * t_b
stat = wstat(t_s, t_b, model, data, off_vec)
print("XSPEC mu_bkg (f * t_b): {}".format(bkg))
print("XSPEC stat: {}".format(stat))
def calc_wstat_xspec():
data, model, staterr, off_vec, alpha = get_test_data()
from xspec_stats import xspec_wstat as wstat
from xspec_stats import xspec_wstat_f, xspec_wstat_d
# alpha = t_s / t_b
t_b = 1. / alpha
t_s = 1
d = xspec_wstat_d(t_s, t_b, model, data, off_vec)
f = xspec_wstat_f(data, off_vec, t_s, t_b, model, d)
bkg = f * t_b
stat = wstat(t_s, t_b, model, data, off_vec)
print("XSPEC mu_bkg (f * t_b): {}".format(bkg))
print("XSPEC stat: {}".format(stat))
def calc_wstat_xspec(mu_sig, n_on, n_off, alpha):
from xspec_stats import xspec_wstat as wstat
from xspec_stats import xspec_wstat_f, xspec_wstat_d
td = test_data()
# alpha = t_s / t_b
t_b = 1. / alpha
t_s = 1
d = xspec_wstat_d(t_s, t_b, mu_sig, n_on, n_off)
f = xspec_wstat_f(n_on, n_off, t_s, t_b, mu_sig, d)
bkg = f * t_b
stat = wstat(t_s, t_b, mu_sig, n_on, n_off)
print("XSPEC mu_bkg (f * t_b): {}".format(bkg))
print("XSPEC stat: {}".format(stat))
def calc_wstat_gammapy(mu_sig, n_on, n_off, alpha):
from gammapy.stats import wstat, get_wstat_mu_bkg, get_wstat_gof_terms
# background estimate
bkg = get_wstat_mu_bkg(mu_sig=mu_sig, n_on=n_on, n_off=n_off, alpha=alpha)
print("Gammapy mu_bkg: {}".format(bkg))
# # without extra terms
# statsvec = wstat(extra_terms=False, mu_sig=mu_sig, n_on=n_on, n_off=n_off,
# alpha = alpha)
#
# print("Gammapy stat: {}".format(np.sum(statsvec)))
# print("Gammapy statsvec: {}".format(statsvec))
#
# print("---> with extra terms")
# extra_terms = _get_wstat_extra_terms(n_on = n_on,
# n_off = n_off)
# print("Gammapy extra terms: {}".format(extra_terms))
statsvec = wstat(extra_terms=True, mu_sig=mu_sig, n_on=n_on, n_off=n_off,
alpha=alpha)
print("Gammapy stat: {}".format(np.sum(statsvec)))
print("Gammapy statsvec: {}".format(statsvec))
def _stat_fcn(self, mu, delta=0, index=None):
return wstat(self.n_on[index], self.n_off[index], self.alpha[index],
mu) - delta
def TS_max(self):
"""Stat value for best fit hypothesis, i.e. expected signal mu = n_on - alpha * n_off"""
return wstat(self.n_on, self.n_off, self.alpha, self.excess)
def TS_null(self):
"""Stat value for null hypothesis, i.e. 0 expected signal counts"""
return wstat(self.n_on, self.n_off, self.alpha, 0)
