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 background(self):
"""Background counts estimated from the marginalized likelihood estimate.
See :ref:`wstat`
"""
mu_bkg = self.alpha.data * get_wstat_mu_bkg(
n_on=self.counts.data,
n_off=self.counts_off.data,
alpha=self.alpha.data,
mu_sig=self.npred_sig().data,
)
return RegionNDMap.from_geom(geom=self._geom, data=mu_bkg)
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))