Find maximum of a function.

Dear all,

I have the following code that aims at maximixing LL_all with respect to "gidraw" which is scalar.

%the data
n=1;
Xfi=[  -1.4+randn(n,1) 0.5+0.6*randn(n,1)];  
beta=[3 2 ]';
yi=randn(n)  ;
gidraw=0.5;
lam=Xfi*beta + gidraw;  
int=yi.*lam-exp(lam);
int=sum(int);

 %the function
  LL_all = -(log(normpdf(gidraw,2,sqrt(0.5)))+int);

So, my question is what is the maximum of LL_all? That is, how can I find the maximum of this function? Also can I calculate the Hessian matrix(which is a scalar more precisely) of this function?

Thanks in advance

[John D'Errico]

Well, first, you would need to define what gidraw is.

[ektor]

thanks John. gidraw is a scalar. For example gidraw=0.5 (see above).

[Walter Roberson]

I thought I understood what you wanted, but lam is an n x 1 vector and yi is an n x n array, so yi .* lam is an error. yi*lam would be well defined and would be n x 1 which would be fine for adding exp(lam) which would be n x 1 as well. The sum() in the next line would then be creating a scalar. Is that what is desired?

[ektor]

Hi Walter, I made a small modification in the above code to make things easier. n=10 now becomes n=1. Yes, this is what is desired. Basically I want to find the posterior mode of LL_all.

Answer 1

[JMP Phillips]

If gidraw is a scalar, your problem doesn't make sense, as LL_all is just a number. If gidraw is vector, the maximum of -[log(normpdf) + int] is +Inf.

[ektor]

Hi JMP, Thanks. I made a small modification, N=10 now becomes N=1. Does this make sense now?

[JMP Phillips]

still confused sorry, your code just returns a number. Don't you need to specify a range of inputs for the distribution, so that you can find the maximum within the range? In your equation for LL_all, which is the vector input, is it Int?