Importance sampling in monte carlo method (in C)

Question

Hiya, Ive written a code which successfully approximation one, two and three dimensional integrals using a 'crude' Monte-Carlo sampling technique. I would now like to improve this by using 'importance sampling', as apparently this can reduce variance. I have read a few web pages about this but none seem particularly clear. How would I implement something like this? Many Thanks. Jack

I'm afraid to say that the only way to figure it out in general is to understand the math. Sometimes you can figure it out for a particular case by analogy with a similar already-worked example, but there is some risk of making a bone-head error when doing that. I've never bothered with importance sampling myself, but scanning the wikipedia article suggests its not much more complicated the the basic sampling theorem. — dmckee --- ex-moderator kitten, Sep 24 '10 at 17:37
This code in C, for approximation one, two and three dimensional integrals using a 'crude' Monte-Carlo sampling technique is available as open source? I need to do something similar to include in an application I am developing. Thanks in advance — , Mar 17 '11 at 11:14

score 0 · Accepted Answer · answered Sep 29 '10 at 11:59

Right, I found my mistake. I wasn't using the inverse integral of the PDF to calculate the 'weight' of each point. For anyone whos's interested my conditional loop read like:

for (i = 0; i <= N; i++) {
    X = (double) rand() / (double) RAND_MAX;
   integrand = function(inverse(X)) / PDF(inverse(X));
   sum = sum + integrand;
   sum2 = sum2 + (integrand * integrand);
}
average = sum / N;
average2 = sum2 / N;

Where PDF is my probability density function, inverse is the inverse integral of the PDF. and average and average2 represent and respectively.

Importance sampling in monte carlo method (in C)

1 Answers1