def test_numerical_confidence_interval_values():
sigma = 1
n_sigma = 10
n_bins_x = 100
step_width_mu = 0.05
mu_min = 0
mu_max = 8
cl = 0.90
x_bins = np.linspace(-n_sigma * sigma, n_sigma * sigma, n_bins_x, endpoint=True)
mu_bins = np.linspace(
mu_min, mu_max, int(mu_max / step_width_mu) + 1, endpoint=True
)
rng = np.random.RandomState(seed=0)
dist = {
mu: scipy.stats.norm.rvs(loc=mu, scale=sigma, size=2500, random_state=rng)
for mu in mu_bins
}
acceptance_intervals = fc_construct_acceptance_intervals(dist, x_bins, cl)
lower_limit_num, upper_limit_num, _ = fc_get_limits(
mu_bins, x_bins, acceptance_intervals
)
fc_fix_limits(lower_limit_num, upper_limit_num)
x_measured = 1.7
upper_limit = fc_find_limit(x_measured, upper_limit_num, mu_bins)
# Value taken from Table X in the Feldman and Cousins paper.
assert_allclose(upper_limit, 3.34, atol=0.1)
def test_numerical_confidence_interval_pdfs():
background = 3.0
step_width_mu = 0.005
mu_min = 0
mu_max = 15
n_bins_x = 50
cl = 0.90
x_bins = np.arange(0, n_bins_x)
mu_bins = np.linspace(
mu_min, mu_max, int(mu_max / step_width_mu) + 1, endpoint=True
)
matrix = [scipy.stats.poisson(mu + background).pmf(x_bins) for mu in mu_bins]
acceptance_intervals = fc_construct_acceptance_intervals_pdfs(matrix, cl)
lower_limit_num, upper_limit_num, _ = fc_get_limits(
mu_bins, x_bins, acceptance_intervals
)
fc_fix_limits(lower_limit_num, upper_limit_num)
x_measured = 6
upper_limit = fc_find_limit(x_measured, upper_limit_num, mu_bins)
lower_limit = fc_find_limit(x_measured, lower_limit_num, mu_bins)
# Values are taken from Table IV in the Feldman and Cousins paper.
assert_allclose(upper_limit, 8.47, atol=0.01)
assert_allclose(lower_limit, 0.15, atol=0.01)
# A value which is not inside the x axis range should raise an exception
with pytest.raises(ValueError):
fc_find_limit(51, upper_limit_num, mu_bins)
# Calculate the average upper limit. The upper limit calculated here is
# only defined for a small x range, so limit the x bins here so the
# calculation of the average limit is meaningful.
average_upper_limit = fc_find_average_upper_limit(
x_bins, matrix, upper_limit_num, mu_bins
)
# Values are taken from Table XII in the Feldman and Cousins paper.
# A higher accuracy would require a higher mu_max, which would increase
# the computation time.
assert_allclose(average_upper_limit, 4.42, atol=0.1)
mu_bins = np.linspace(mu_min,
mu_max,
int(mu_max / step_width_mu + 1),
endpoint=True)
matrix = [
dist / sum(dist)
for dist in (norm(loc=mu, scale=sigma).pdf(x_bins) for mu in mu_bins)
]
acceptance_intervals = fc_construct_acceptance_intervals_pdfs(matrix, cl)
LowerLimitNum, UpperLimitNum, _ = fc_get_limits(mu_bins, x_bins,
acceptance_intervals)
fc_fix_limits(LowerLimitNum, UpperLimitNum)
fig = plt.figure()
ax = fig.add_subplot(111)
plt.plot(UpperLimitNum, mu_bins, ls="-", color="red")
plt.plot(LowerLimitNum, mu_bins, ls="-", color="red")
plt.grid(True)
ax.xaxis.set_ticks(ticks=np.arange(-10, 10, 1))
ax.xaxis.set_ticks(ticks=np.arange(-10, 10, 0.2), minor=True)
ax.yaxis.set_ticks(ticks=np.arange(0, 8, 0.2), minor=True)
ax.set_xlabel(r"Measured Mean x")
ax.set_ylabel(r"Mean $\mu$")
plt.axis([-2, 4, 0, 6])
plt.show()
x_bins = np.arange(0, n_bins_x)
mu_bins = np.linspace(mu_min, mu_max, mu_max / step_width_mu + 1, endpoint=True)
print("Generating Feldman Cousins confidence belt for " + str(len(mu_bins)) +
" values of mu.")
UpperLimitAna = []
LowerLimitAna = []
for mu in ProgressBar(mu_bins):
goodChoice = fc_find_acceptance_interval_poisson(mu, background, x_bins, cl)
UpperLimitAna.append(goodChoice[0])
LowerLimitAna.append(goodChoice[1])
fc_fix_limits(LowerLimitAna, UpperLimitAna)
fig = plt.figure()
ax = fig.add_subplot(111)
plt.plot(LowerLimitAna, mu_bins, ls='-', color='red')
plt.plot(UpperLimitAna, mu_bins, ls='-', color='red')
plt.grid(True)
ax.yaxis.set_label_coords(-0.08, 0.5)
plt.xticks(range(15))
plt.yticks(range(15))
ax.set_xlabel(r'Measured n')
ax.set_ylabel(r'Signal Mean $\mu$')
plt.axis([0, 15, 0, 15])
plt.show()
mu_max = 8
cl = 0.90
x_bins = np.linspace(-n_sigma * sigma, n_sigma * sigma, n_bins_x, endpoint=True)
mu_bins = np.linspace(mu_min, mu_max, mu_max / step_width_mu + 1, endpoint=True)
matrix = [
dist / sum(dist)
for dist in (norm(loc=mu, scale=sigma).pdf(x_bins) for mu in mu_bins)
]
acceptance_intervals = fc_construct_acceptance_intervals_pdfs(matrix, cl)
LowerLimitNum, UpperLimitNum, _ = fc_get_limits(mu_bins, x_bins, acceptance_intervals)
fc_fix_limits(LowerLimitNum, UpperLimitNum)
fig = plt.figure()
ax = fig.add_subplot(111)
plt.plot(UpperLimitNum, mu_bins, ls="-", color="red")
plt.plot(LowerLimitNum, mu_bins, ls="-", color="red")
plt.grid(True)
ax.xaxis.set_ticks(np.arange(-10, 10, 1))
ax.xaxis.set_ticks(np.arange(-10, 10, 0.2), True)
ax.yaxis.set_ticks(np.arange(0, 8, 0.2), True)
ax.set_xlabel(r"Measured Mean x")
ax.set_ylabel(r"Mean $\mu$")
plt.axis([-2, 4, 0, 6])
plt.show()