1

Monte Carlo integration works by randomly sampling within the interval of integration and is known that as the number of samples tends towards infinity that it will converge on the right answer.

I've heard that if you use uniform sampling instead of random sampling that it isn't garaunteed to converge on the right answer.

Why is that?

My best guess is that uniform sampling is limited to sampling rational numbers, while random sampling has no such limitation.

Is that it / am I close? Or is it something else?

Alan Wolfe
  • 1,299
  • 6
    Depending on how you intend "uniform sampling", this is quite similar to the Midpoint Rule for numerical integration. In any case Monte Carlo integration is not certain to converge on the right answer, only to converge with probability tending to one as the sample size increases. – hardmath May 13 '17 at 18:58
  • 1
    Convergence is not an issue in this comparison, but the convergence rate. With the uniform grid one needs much more function evaluations to reach the same error level. Look at the similar question here. – A.Γ. May 14 '17 at 11:31

0 Answers0