Importance sampling in monte carlo method (in C)
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05-10-2019 - |
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
Solution
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.
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