def getFCErr(n, bkg=0, MaxN=25):
Nbknd = bkg
x_bins = np.arange(0, 50)
mu_bins = np.linspace(0,
MaxN,
np.int(np.round(MaxN / 0.005 + 1, 0)),
endpoint=True)
matrix = [stats.poisson(mu + Nbknd).pmf(x_bins) for mu in mu_bins]
acceptance_intervals = gstats.fc_construct_acceptance_intervals_pdfs(
matrix, 0.6827)
LowerLimitNum, UpperLimitNum, _ = gstats.fc_get_limits(
mu_bins, x_bins, acceptance_intervals)
#print(matrix)
#print(mu_bins)
#print(LowerLimitNum)
#print(UpperLimitNum)
N = n
ul = gstats.fc_find_limit(N, UpperLimitNum, mu_bins)
ll = gstats.fc_find_limit(N, LowerLimitNum, mu_bins)
#print(ll)
#print(ul)
return ll, ul
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)
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)
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)
for imu_b, mu_b in enumerate(mu_barray):
B2v = (T0vS / T2v) * (sigma / Qbb)**6
n = 0.5 * (2.8 +
10**(-0.48 - 0.32 * np.log10(mu_b * sigma * M * T) - 0.046 *
(np.log10(mu_b * sigma * M * T))**2))
aB = mu_b * M * T * 2 * n * sigma
Barray[imu_b] = aB + B2v
narray[imu_b] = n
eff = sp.erf(n / np.sqrt(2))
#Brand = np.random.poisson( aB + B2v, 1000)
x_bins = np.arange(0, 100)
mu_bins = np.linspace(0, 50, int(50 / 0.1) + 1, endpoint=True)
matrix = [stats.poisson(mu + aB + B2v).pmf(x_bins) for mu in mu_bins]
acceptance_intervals = gstats.fc_construct_acceptance_intervals_pdfs(
matrix, 0.9)
LowerLimitNum, UpperLimitNum, _ = gstats.fc_get_limits(
mu_bins, x_bins, acceptance_intervals)
sarr = np.zeros(1000)
for ex in np.arange(1, 1000, 1):
sarr[ex] = gstats.fc_find_limit(np.random.poisson(aB + B2v),
UpperLimitNum, mu_bins)
s = np.median(sarr)
Thalfarray[isig, imu_b] = T0vS * eff_tot * eff / s
#Thalfarray[imu_b] = T0vS*eff/s
Sarray[imu_b] = s
#matplotlib.rcParams['font.sans-serif'] = "Helvetica"
font = {
'weight': 'normal', #'family' : 'sans-serif'
'size': 15
n_sigma = 10
n_bins_x = 1000
step_width_mu = 0.005
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, 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)
