Monte Carlo

[EDIT: Thu May 12 22:03:30 UTC 2011 Duplicate Removed - MKF]

Hey guys,

how can I let certain parameters in my model have a range using Monte Carlo simulations?

I have a relatively simple model and I would want to designate a range to certain parameters. I would like to create scenarios like holding one parameter in its lowest part of the range while another in its highest part, etc.

Cheers, Ruben

Answer 1

[Oleg Komarov]

This example is what you're looking for: http://www.vertex42.com/ExcelArticles/mc/MatlabMCExample.html

MC is computationally heavy. For this example taken from the link I repeat the procedure 100,000 times drawing samples of 1000. It takes 13 seconds using very low amount of memory.

In MC in general the more you have the better, thus you could optimize this example to generate rand(n,something) to fit the 80% of your memory and reduce the number of loops.

tic
n = 1000;
l = 1e5;
s.ymean = zeros(n,1);
s.ystd  = s.ymean;

for ii = 1:l
    x1 = randn(n,1) * 5  + 100;
    x2 = rand (n,1) * 10 + 5;
    y = x2.^2 ./ x1;

      s.ymean(ii) = mean(y);
      s.ystd (ii) = std(y);
  end

toc

[Ruben Verkempynck]

Thank you very much, this is a clear example.

Another question:

How many samples from the ranges would you propose?

I tried ten thousand but my computer almost lost its memory.

I am running Matlab 2009a on a MacBook from 2008

[Oleg Komarov]

Did you use randn(10000)? Thats almost 763 MB and 10,000 samples of 10,000 draws.

[Ruben Verkempynck]

Sorry, I meant rand(10000), without the n

[Ruben Verkempynck]

Maybe it is easier if I just post the code, sorry:

% Monte Carlo simulation of variable parameters

clear all

close all

pe_alles = 200+200*rand(10000,1);

pt_alles = 80+20*rand(10000,1);

ce_alles = 2547+1000*rand(10000,1);

ct_alles = 450+200*rand(10000,1);

for i = 1:10000

pe = pe_alles(i);

pt = pt_alles(i);

ce = ce_alles(i);

ct = ct_alles(i);

Herring_Baltic

end

You see, I have a function Herring_baltic that uses parameters that are a matrix (10,000,1) filled with random samples.

How did you repeat the example 100,000 times each time drawing 1000 samples? Did you create another loop over the example?

[Oleg Komarov]

100,000 samples of 1000 observations.

I don't see any problem in your code with regards to memory. Do you still have memory problems, then You need to inspect your function.

Or post a new thread asking to optimize it.