how to do sensitivity analysis of three variables using MATLAB

Dear friends,

How to do sensitivity analysis for this formula? There are three variables A, B and C.

Your help would be highly appreciated.

Answer 1

[Alan Stevens]

Depends what your measure of sensitivity is. One possibility is to do a Monte-Carlo simulation and use the standard error on the mean as the measure. For example:

m = 1000;
Yfn = @(A,B,C) (-1.8*A + 0.025*B + 0.33*C + 0.0025*m)./(1 - 1.13*A + 0.011*B);

% Constraints - assuming the constants A, B and C are uniformly 
% distributed between lower and upper limits.

N = 10^6;  % Number of trials
A = pi/36 + rand(N,1)*(pi/6 - pi/36);
B = 20 + rand(N,1)*40;
C = 1.6 + rand(N,1)*3.4;

Y = Yfn(A,B,C);  % N values of Y

Yav = mean(Y);           % average value of Y
sigma = std(Y);          % standard deviation 
se = sigma/sqrt(N);  % standard error 

disp('    Yav          se')

    Yav          se

disp([Yav se])

    3.7472    0.0005

Or use the standard deviation as the measure.

Or, if you want the sensitivity to each parameter separately, then do the same as the above for each separately keeping the other two fixed at their nominal values.