maximize a log-likelihood function

Hi all,

I am looking for an advice in regards the following task:

I've set up a function

    function proba = pdf(x,a,b,c,d);

where a,b,c,d are scalars and x a vector. So far I am happy with the output.

After defining the log-likelihood function in a separate function-m file such as:

    %_llik.m
    function loglik=_llik(theta,data);
    loglik=-sum(log(pdf(data,theta1,theta2,theta3,theta4)));

I've run from a script file (optimization without constraints):

    theta0=[1.3,0.89,0.034,0.0056]
    [theta_eq,fval,exitflag,output,grad,hessian] = ... 
    fminunc(@(theta) _llik(theta,data),theta0)

 that unfortunately returns:

    Undefined function '_llik' for input arguments of type 'double'.
    Error in @(theta) _llik(theta,data)
    Error in fminunc (line 254)
    f = feval(funfcn{3},x,varargin{:});
    Caused by:
    Failure in initial user-supplied objective function evaluation. FMINUNC cannot continue.
    Error using edit (line 66)
    Undefined function or variable 'theta'.

Hence my questions:

1/ are the errors due to my function proba which should be re-built in array terms such as:

    function proba = pdf(data,theta(1),theta(2),theta(3),theta(4));

2/ Having read a bit of documentation on @fmincon, is it possible 'clearly' to illustrate how can I add constraints on

    0<theta(1)<=2;
   -1<=theta(2)<=1;
    0<=theta(3)<=+inf; 
   -inf<=theta(4)<=+inf; % belongs to R not sure if it's worth constraining it to -inf;+inf

Actually I am not sure if i can set:

lb=[0,-1,0,-inf] and ub = [2,1,+inf,+inf]

Thanks in advance

[David Young]

Might be a red herring, but I wonder about that initial underscore. Is it in the m-file name? If so, could there be a system problem with filenames beginning with underscore that stops their being found? Might be worth the experiment of renaming the file and the function.

Answer 1

[Alan Weiss]

You are quite right, the way to keep the function from stepping out of bounds is to set the bounds exactly as you guessed:

 lb = [0,-1,0,-Inf];
 ub = [2,1,Inf,Inf];

Make sure that you pass the bounds to fmincon correctly:

 [x,fval,exitflag] = fmincon(@_llik,theta0,[],[],[],[],lb,ub)

Alan Weiss

MATLAB mathematical toolbox documentation