StatRed: Added some work-in-progress code.

statred/ass1/lab_exercises.py

+#from math import mean
+#import matplotlib.pyplot as plt
+from numpy.random import multivariate_normal
 
+def mu_est(x):
+    return sum(x) / float(len(x))
+
+def cov_est(x):
+    avg = mean(x)
+    n = len(x)
+    # TODO: transpose the second "(i - avg)"
+    return sum([(i - avg)*(i - avg) for i in x]) / float(n-1)
+
+mean = [0,0]
+cov  = [[1,0],[0,100]] # diagonal covariance, points lie on x or y-axis
+N    = 512 # Samples to use.
+
+x,y = multivariate_normal(mean, cov, N).T
+print 'x:', x
+print 'y:', y
+
+print 'mu_est(x):', mu_est(x)
+print 'mu_est(y):', mu_est(y)

statred/multivariate.py

+mean = [0,0]
+cov = [[1,0],[0,100]] # diagonal covariance, points lie on x or y-axis
+
+import matplotlib.pyplot as plt
+import numpy as np
+x,y = np.random.multivariate_normal(mean, cov, 5000).T
+print 'x:', x
+print 'y:', y
+plt.plot(x,y,'x'); plt.axis('equal'); plt.show()
+

statred/mvnd.py

+from numpy import pi, exp, power, dot, rank
+from numpy.linalg import inv, det
+
+def mvnd(x, mu, S):
+    """
+    Calculate multivariate normal distribution of vector X, given mu (mean of
+    elements in vector X) and S (covariance matrix).
+
+    Based on the following formula:
+    http://upload.wikimedia.org/math/a/0/a/a0ad9db46854c4a616ce6959095cf21d.png
+    """
+    return exp((2 * pi) ** rank(x)) * power(det(S), -.5) \
+            * exp(-.5 * dot(dot((x - mu).T, inv(S)), (x - mu)))
+
+#mean = [0,0]
+#cov = [[1,0],[0,100]] # diagonal covariance, points lie on x or y-axis
+#
+#import matplotlib.pyplot as plt
+#import numpy as np
+#x,y = np.random.multivariate_normal(mean,cov,5000).T
+##mvnd(x, mean, cov)
+#plt.plot(x,y,'x'); plt.axis('equal'); plt.show()
+

statred/urls.txt

+http://docs.scipy.org/doc/numpy/reference/generated/numpy.random.multivariate_normal.html
+http://packages.python.org/algopy/examples/covariance_matrix_computation.html
+http://en.wikipedia.org/wiki/Multivariate_normal_distribution
+http://lmf-ramblings.blogspot.com/2009/07/multivariate-normal-distribution-in.html