Normal MLE using fminunc

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Jen 2011-8-26

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https://ww2.mathworks.cn/matlabcentral/answers/14601-normal-mle-using-fminunc

Hi,

I am using the following code to estimate the MLE for the normal distribution.

load normaldata.dat
global x N
x = normaldata;
N = length(x);
theta0 = zeros(2,1);
[thetac,fval,output] = fminunc(@Norm,theta0);
thetac(2) = exp(thetac(2)); 
function output = NORM(theta)
   global x N
   theta(2) = exp(theta(2)); 
   output = 0;
   
   for n = 1:N
      output = output + (1/(2*theta(2)))*(-(x(n)-theta(1))^2);
   end
   
   output = output - ((N/2)*(log(theta(2))));
   output = -output;
   end

It gives me the right answer, but I dont understand why we are setting sigma to exp(sigma) (refer to lines 7 and 10). Im guessing because we want sigma to be positive, in which case I understand why theta(2) = exp(theta(2)) in line 10 is present. But what is the relevance of theta(2) = exp(theta(2)) in line 7, surely it should be theta(2) = log(theta(2))???