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()