add bootstrap example

tests/test_bootstrap_train.py

@@ -0,0 +1,50 @@
+# Boostrapped AI models at training stage example
+#
+# Run with: python filename.py
+#
+# [email protected], 2024
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+N = 1000    # Number of events
+B = 50      # Number of bootstrap trained AI models
+
+# Generate some dummy data
+eta         = np.random.normal(loc=0, scale=1.5, size=N)   # Observable of interest
+weights     = np.random.uniform(0.0, 1.0, size=N)          # Default AI model weights
+weights_BS  = np.random.uniform(0.0, 1.0, size=(N, B))     # Bootstrap trained AI model weights
+
+# Define histogram bins
+bins = np.linspace(-4, 4, 21)  # Example bin edges
+bin_centers = 0.5 * (bins[:-1] + bins[1:])
+
+# Compute the original histogram
+orig_h, _ = np.histogram(eta, bins=bins, weights=weights)
+
+# Compute histograms for each bootstrap trained AI model
+histograms = np.array([
+    np.histogram(eta, bins=bins, weights=weights_BS[:, c])[0]
+    for c in range(B)
+])
+
+# Compute standard deviation across different AI models as a simple proxy measure
+std_BS = np.std(histograms, axis=0)
+
+# Compute percentile bootstrap for 1 sigma, protect non-nested intervals with abs
+# and symmetrize (average) over upper/lower interval
+lo_BS  = np.percentile(histograms, q=16, axis=0)
+hi_BS  = np.percentile(histograms, q=84, axis=0)
+prc_BS = np.array([np.abs(lo_BS - orig_h), np.abs(hi_BS - orig_h)])
+prc_BS = np.mean(prc_BS, axis=0)
+
+# Plot the original histogram with bootstrap error bars
+plt.errorbar(x=bin_centers, y=orig_h, yerr=std_BS, fmt='s', color='black', label='$\\pm 1 \\sigma$ (std)', lw=8.0)
+plt.errorbar(x=bin_centers, y=orig_h, yerr=prc_BS, fmt='s', color='red',   label='$\\pm 1 \\sigma$ (symmetrized prc)', lw=2.5)
+
+plt.xlabel("Observable $x$")
+plt.ylabel("Weighted Count")
+plt.ylim([0,None])
+plt.title(f'Number of events = {N}, Number of bootstrap trained models = {B}')
+plt.legend()
+plt.show()