Prob_H = 0.08
Prob_E_given_H = 0.95
Prob_E_given_Hc = 0.07

Prob_Hc = 1 - Prob_H
Prob_E = Prob_E_given_H * Prob_H + Prob_E_given_Hc * Prob_Hc

Prob_H_given_E = Prob_E_given_H * Prob_H / Prob_E

print(Prob_H_given_E)

import numpy as np
import matplotlib.pyplot as plt

plt.figure(figsize=(10,10))
size = 0.35

inner_vals = np.array([Prob_H, 1-Prob_H])
vals1 = np.array([Prob_E_given_H, 1-Prob_E_given_H])*Prob_H
vals2 = np.array([Prob_E_given_Hc, 1-Prob_E_given_Hc])*Prob_Hc
outer_vals = np.hstack((vals1, vals2))

cmap = plt.get_cmap("tab20c")
inner_colors = cmap([4, 0])
outer_colors = cmap([5, 6, 1, 2])

outer_labels = 'positive | ill', 'negative | ill', \
'positive | well', 'negative | well'
plt.pie(outer_vals, radius=1, colors=outer_colors,
       wedgeprops=dict(width=size, edgecolor='w'), labels=outer_labels,
       explode=(0.05, 0, 0.05, 0))
plt.legend()
inner_labels = r'$H$', r'$H^c$'
plt.pie(inner_vals, radius=1-size, colors=inner_colors,
       wedgeprops=dict(width=size, edgecolor='w'), autopct='%1.1f%%' )
plt.show()

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

# Define the mean and covariance matrix
mean = np.array([0, 0])
cov = np.array([[2, 0.8], [0.8, 1]])
invcov = np.linalg.inv(cov)

# Create a meshgrid for plotting
x1 = np.linspace(-4, 4, 100)
x2 = np.linspace(-4, 4, 100)
X1, X2 = np.meshgrid(x1, x2)

# Calculate the Gaussian density function
def gaussian_density(x, mean, covariance):
    x_minus_mean = x - mean
    exponent = -0.5*np.dot(np.dot(x_minus_mean.T, invcov), x_minus_mean)
    coefficient = 1/((2*np.pi)**(len(mean)/2)*np.sqrt(np.linalg.det(cov)))
    return coefficient * np.exp(exponent)

Z = np.zeros((len(x1), len(x2)))
for i in range(len(x1)):
    for j in range(len(x2)):
        x = np.array([X1[i, j], X2[i, j]])
        Z[i, j] = gaussian_density(x, mean, cov)

# Create the figure and subplots
fig = plt.figure(figsize=(11, 5), dpi=100)
ax1 = fig.add_subplot(121, projection='3d')
ax2 = fig.add_subplot(122)

# Surface plot
ax1.plot_surface(X1, X2, Z, cmap=cm.viridis)
ax1.set_xlabel('$x_1$')
ax1.set_ylabel('$x_2$')
ax1.set_zlabel('$p(x)$')
ax1.set_title('Gaussian density function')

# Contour plot
contour = ax2.contour(X1, X2, Z, levels=10)
ax2.set_xlabel('$x_1$')
ax2.set_ylabel('$x_2$')
ax2.set_title('Contour of Gaussian density function')
ax2.axis('square')
ax2.grid()
fig.tight_layout()
plt.show()

fig = plt.figure(figsize=(11, 5), dpi=100)
ax1 = fig.add_subplot(121, projection='3d')
ax2 = fig.add_subplot(122)

# Surface plot
ax1.plot_surface(X1, X2, Z, cmap=cm.viridis, alpha=0.8)
ax1.plot(X1[25,:], X2[25,:], Z[25,:], color='red', linewidth=3, alpha=1)
ax1.set_xlabel('$x_1$')
ax1.set_ylabel('$x_2$')
ax1.set_zlabel('$p(x)$')
ax1.set_title('Gaussian density function')

# Contour plot
contour = ax2.contour(X1, X2, Z, levels=10)
ax2.axhline(-2, color='red', linewidth=4, alpha=0.5)
ax2.plot(x2*0.8, x2, ':')
ax2.set_xlabel('$x_1$')
ax2.set_ylabel('$x_2$')
ax2.set_title('Contour of Gaussian density function')
ax2.axis('square')
ax2.grid()
fig.tight_layout()
plt.show()

# Conditional pdf plot
plt.figure(figsize=(5, 3), dpi=100)
plt.plot(X1[25,:], Z[25,:], color='red', linewidth=4, alpha=0.3)
plt.xlabel('$x_1$')
plt.ylabel('$p(x_1|x_2=-2)$')
plt.title('Conditional density function (scaled)')
plt.grid()
plt.show()