Passing data through fminsearch

I want to use fminsearch to fit parameters to a model. I'm not sure, however, the best method to pass data through fminsolve. Currently I'm passing data through as a global variable although I have previously been advised to avoid defining globals whenever possible. For a minimal working example I minimize the residual sum of squares to find the mean below. Any comments on why I should not use a global variable and what I can do instead.

Thanks, Cameron

% Estimate mean by minimizing residual sum of squares through fminsolve

% Define data global
global y 

% generate one hundred draws of mean 100 alongside a standard normal error term
y = 100 + randn(100,1) ;

% initial parameter guess 
par_0 = [0]         ;

% Define fminsolve
[par_hat , rss] = fminsearch(@min_rss, par_0) ;

% Residual sum of squares function 
function rss = min_rss(par)    
    global y 
    rss = [y - par]'*[y - par] ;
end 

Answer 1

[Stephen23]

You should definitely avoid global variables.

For your situation the easiest way to parameterize a function is to use a simple anonymous function:

% generate one hundred draws of mean 100 alongside a standard normal error term:
y = 100 + randn(100,1);
% Call fminsolve:
fun = @(v) min_rss(v,y); % anonymous function
[par_hat, rss] = fminsearch(fun, 0)
% Residual sum of squares function:
function rss = min_rss(par,y)     
    rss =  (y - par)' * (y - par);
end

Giving:

par_hat =
  100.1231
rss =
  133.7660

Note that I also replaced your square brackets in the function with the correct grouping operator (parentheses), exactly as the MATLAB Editor recommended (you should always pay attention to the warnings shown by the editor).

Answer 2

[Jeff Miller]

One way is to nest the rss function:

function [ par_hat , rss ] = finder
    % A wrapper function to avoid globals
    
    y = 100 + randn(100,1) ;
    % initial parameter guess
    par_0 = [0]         ;
    % Define fminsolve
    [par_hat , rss] = fminsearch(@min_rss, par_0) ;
    
    % Residual sum of squares function
    function rss = min_rss(par)
        rss = [y - par]'*[y - par] ;
    end
    
end