max_likelihood_2_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, 10, 0.1)
Y = np.arange(0.01, 10, 0.1)
X, Y = np.meshgrid(X, Y)

Z = norm(X, Y).pdf(5) * norm(X, Y).pdf(6)
mina = np.array(Z).reshape(1,-1)
print(max(mina[0]))
# Plot the surface.
surf = ax.plot_surface(X, Y, Z, cmap=cm.coolwarm, alpha=0.4,
                       linewidth=0.2, antialiased=False)


# Customize the z axis.
ax.set_zlim(0, 0.2)
ax.set_xlim(-1, 10)
ax.set_ylim(-1, 10)
ax.zaxis.set_major_locator(LinearLocator(5))
ax.set_zticklabels([])

ax.view_init(30, 25)
ax.set_xlabel('$\mu$')
ax.set_ylabel('$\sigma$')
ax.set_zlabel('$p(5 | \mu, \sigma)$  X  $p(6 | \mu, \sigma) $')
# Add a color bar which maps values to colors.

plt.show()