Monte Carlo integration uses Monte Carlo methods to perform numerical integration. With Monte Carlo integration, we estimate value of integral using random sampling of function

  • Value of estimate depends on random sample used
  • But algorithm gives the correct value of integral “on average”

Since Monte Carlo Integration only requires function to be evaluated at random points on its domain, it is applicable to functions with discontinuities, and functions that are impossible to integrate directly.

Another property of Monte Carlo is that error of estimate is independent of the dimensionality of the integrand (no curse of dimensionality). This property makes Monte Carlo the only practical numerical integration algorithm for high-dimensional integrals. The error only depends on the number of random samples used, and it decreases at a rate of in the number of samples.

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