updating lectures

doc/src/Regression/Bootstrap.py

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+from numpy import *
+from numpy.random import randint, randn
+from time import time
+import matplotlib.mlab as mlab
+import matplotlib.pyplot as plt
+
+# Returns mean of bootstrap samples                                                                                                                                                
+def stat(data):
+    return mean(data)
+
+# Bootstrap algorithm
+def bootstrap(data, statistic, R):
+    t = zeros(R); n = len(data); inds = arange(n); t0 = time()
+    # non-parametric bootstrap         
+    for i in range(R):
+        t[i] = statistic(data[randint(0,n,n)])
+
+    # analysis    
+    print("Runtime: %g sec" % (time()-t0)); print("Bootstrap Statistics :")
+    print("original           bias      std. error")
+    print("%8g %8g %14g %15g" % (statistic(data), std(data),mean(t),std(t)))
+    return t
+
+
+mu, sigma = 100, 15
+datapoints = 10000
+x = mu + sigma*random.randn(datapoints)
+# bootstrap returns the data sample                                    
+t = bootstrap(x, stat, datapoints)
+# the histogram of the bootstrapped  data                                                                                                    
+n, binsboot, patches = plt.hist(t, 50, facecolor='red', alpha=0.75)
+
+# add a 'best fit' line  
+#y = mlab.normpdf( binsboot, mean(t), std(t))
+#lt = plt.plot(binsboot, y, 'r--', linewidth=1)
+plt.xlabel('Smarts')
+plt.ylabel('Probability')
+plt.axis([95, 105, 0, 10.0])
+plt.grid(True)
+
+plt.show()
+