example_fc_gauss_analytical.py

"""Analytical solution for Gaussian with a boundary at
   the origin. Produces Fig. 10 from the Feldman Cousins
   paper."""
import numpy as np
import matplotlib.pyplot as plt
from astropy.utils.console import ProgressBar

from gammapy.stats import (
    fc_find_acceptance_interval_gauss,
    fc_fix_limits,
)

sigma = 1
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)

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_gauss(mu, sigma, 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.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()