how can I do a maximum likelihood regression using scipy.optimize.minimize

Question

How can I do a maximum likelihood regression using scipy.optimize.minimize? I specifically want to use the minimize function here, because I have a com

Answer 1

Thank you Aleksander. You were correct that my likelihood function was wrong, not the code. Using a formula I found on wikipedia I adjusted the code to:

import numpy as np
from scipy.optimize import minimize

def lik(parameters):
    m = parameters[0]
    b = parameters[1]
    sigma = parameters[2]
    for i in np.arange(0, len(x)):
        y_exp = m * x + b
    L = (len(x)/2 * np.log(2 * np.pi) + len(x)/2 * np.log(sigma ** 2) + 1 /
         (2 * sigma ** 2) * sum((y - y_exp) ** 2))
    return L

x = np.array([1,2,3,4,5])
y = np.array([2,5,8,11,14])
lik_model = minimize(lik, np.array([1,1,1]), method='L-BFGS-B')
plt.scatter(x,y)
plt.plot(x, lik_model['x'][0] * x + lik_model['x'][1])
plt.show()

Now it seems to be working.

Thanks for the help!