Merge pull request #19 from fact-project/calc_sensitivity

Add function to calculate sensitivity in bins and bootstrap

Author: maxnoe

irf/sensitivity.py

@@ -3,6 +3,8 @@
 from fact.analysis import li_ma_significance
 from scipy.optimize import newton
 import warnings
+import pandas as pd
+from scipy.stats import norm
 
 
 @u.quantity_input(t_obs=u.hour, t_ref=u.hour)
@@ -11,7 +13,7 @@ def relative_sensitivity(
     n_off,
     alpha,
     t_obs,
-    t_ref=50*u.hour,
+    t_ref=u.Quantity(50, u.hour),
     target_significance=5,
     significance_function=li_ma_significance,
     initial_guess=0.5,
@@ -99,3 +101,92 @@ def equation(relative_flux):
         'significance_function',
     ]
 )
+
+
+@u.quantity_input()
+def calculate_sensitivity(
+    df,
+    theta2_cut,
+    e_min: u.TeV,
+    e_max: u.TeV,
+    n_bins,
+    t_obs: u.hour,
+    t_ref: u.hour,
+    n_bootstrap=100,
+    min_events=5,
+):
+    theta_cut = np.sqrt(theta2_cut)
+
+    def select_on(df):
+        return df.theta_deg <= theta_cut
+
+    def select_off(df):
+        m = df['theta_deg_off_1'] <= theta_cut
+        for i in range(2, 6):
+            m |= df[f'theta_deg_off_{i}'] <= theta_cut
+        return m
+
+    df = df.copy()
+    if 'weight' not in df.columns:
+        df['weight'] = 1
+
+    bin_edges = np.logspace(np.log10(e_min / u.GeV), np.log10(e_max / u.GeV), n_bins + 1)
+    bin_edges = np.append(-np.inf, np.append(bin_edges, np.inf))
+    bin_id = np.arange(n_bins + 2) + 1
+
+    df['bin'] = np.digitize(df['gamma_energy_prediction'].values, bin_edges)
+
+    sensitivity = pd.DataFrame(index=bin_id)
+    sensitivity['e_low'] = bin_edges[:-1]
+    sensitivity['e_high'] = bin_edges[1:]
+    sensitivity['e_center'] = 0.5 * (sensitivity['e_low'] + sensitivity['e_high'])
+    sensitivity['e_width'] = np.diff(bin_edges)
+    sensitivity['n_on_weighted'] = 0
+    sensitivity['n_off_weighted'] = 0
+    sensitivity['n_on'] = 0
+    sensitivity['n_off'] = 0
+    sensitivity.index.name = 'bin'
+
+    sensitivities = []
+    for i in range(n_bootstrap):
+        cur_sensitivity = sensitivity.copy()
+
+        sampled = df.sample(len(df), replace=True)
+        for bin_id, g in sampled.groupby('bin'):
+            on = select_on(g)
+            off = select_off(g)
+
+            cur_sensitivity.loc[bin_id, 'n_on_weighted'] = g.loc[on, 'weight'].sum()
+            cur_sensitivity.loc[bin_id, 'n_off_weighted'] += g.loc[off, 'weight'].sum()
+            cur_sensitivity.loc[bin_id, 'n_on'] = on.sum()
+            cur_sensitivity.loc[bin_id, 'n_off'] = off.sum()
+
+        cur_sensitivity['relative_sensitivity'] = relative_sensitivity(
+            cur_sensitivity['n_on_weighted'],
+            cur_sensitivity['n_off_weighted'],
+            alpha=0.2,
+            t_obs=t_obs,
+        )
+        cur_sensitivity['iteration'] = i
+
+        sensitivities.append(cur_sensitivity.reset_index())
+
+    sensitivities = pd.concat(sensitivities)
+
+    # aggregate bootstrap samples
+    grouped = sensitivities.groupby('bin')
+    keys = ['n_on', 'n_off', 'n_on_weighted', 'n_off_weighted', 'relative_sensitivity']
+    for key in keys:
+        sensitivity[key] = grouped[key].median()
+        sensitivity[key + '_uncertainty_low'] = grouped[key].quantile(norm.cdf(-1))
+        sensitivity[key + '_uncertainty_high'] = grouped[key].quantile(norm.cdf(1))
+    sensitivity['count'] = grouped['relative_sensitivity'].count()
+
+    invalid = (
+        (sensitivity['n_on'] < min_events)
+        | (sensitivity['n_off'] < min_events)
+        | (sensitivity['count'] / n_bootstrap <= 0.95)
+    )
+    sensitivity.loc[invalid, 'relative_sensitivity'] = np.nan
+
+    return sensitivity