Max_likelihood_one_datapoint.py

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import numpy as np
from scipy.stats import norm

fig = plt.figure()
ax = fig.gca(projection='3d')

# Make data.
X = np.arange(0.01, 5, 0.1)
Y = np.arange(0.01, 5, 0.1)
X, Y = np.meshgrid(X, Y)

Z = norm(X, Y).pdf(5)

# Plot the surface.
surf = ax.plot_surface(X, Y, Z, cmap=cm.coolwarm, alpha=0.4,
                       linewidth=0.2, antialiased=False)
ax.plot((4.91, 4.91), (0, 5), (0, 0), 'r')
ax.plot((0, 5), (0.11, 0.11), (0, 0), 'r')

# Customize the z axis.
ax.set_zlim(0, 2.8)
ax.zaxis.set_major_locator(LinearLocator(5))

ax.view_init(40, 30)
ax.set_xlabel('$\mu$')
ax.set_ylabel('$\sigma$')
ax.set_zlabel('$p(5 | \mu, \sigma)$')
# Add a color bar which maps values to colors.
fig.colorbar(surf, shrink=0.5, aspect=5)

plt.show()