load('./SysID_Exercise_1.mat')

w = [x.' ; 2.*x.'.^2-1].';

theta_ml = inv(w.' * w) * w.'*(y-0.2);

u = [1; 0.4];
sigma_p = 0.01;
sigma = 0.1;

theta_map = inv(1/sigma * w.' * w + 1/sigma_p*eye(2)) * (1/sigma*w.'*(y-0.2)+u/sigma_p);

y_hat_ml = theta_ml(1) * x_v + theta_ml(2) * (2.*x_v.^2-1)+0.2;
y_hat_map = theta_map(1) * x_v + theta_map(2) * (2.*x_v.^2-1)+0.2;

MSE_MLE = sum((y_hat_ml - y_v).^2) / length(y_v)
MSE_MAP = sum((y_hat_map - y_v).^2) / length(y_v)