Lecture1

Likehood possibility

\[L(H|E) = P(E|H) \]

import matplotlib.pyplot as plt
import numpy as np
import scipy.stats

mu = 3.0
sigma = 0.5

data = np.random.randn(100000) * sigma + mu

hx, hy, _ = plt.hist(data, bins=50,color="lightblue")

plt.ylim(0.0,max(hx)+0.05)
plt.title(r'Normal distribution $\mu_0 = 3$ and $\sigma_0 = 0.5$')
plt.grid()

Calculate the log-likelihood

scipy.stats.norm.pdf(6,2.0,1.0)

print( np.log(scipy.stats.norm.pdf(data,2.0,1.0)).sum() )

x = np.linspace(-10, 10, 1000, endpoint=True)

y = []
for i in x:
    y.append(np.log(scipy.stats.norm.pdf(data,i,0.5)).sum())

plt.plot(x,y)

plt.title(r'Log-Likelihood')
plt.xlabel(r'$\mu$')

plt.grid()

-154314.14596206427

print('mean ---> ', np.mean(data))
print('std deviation ---> ', np.std(data))

mean --->  2.999606326069087
std deviation --->  0.4991923934863224

y_min = y.index(max(y))
print('mean (from max log likelohood) ---> ', x[y_min])

mean (from max log likelohood) --->  2.9929929929929937