In mathematics, Monte Carlo integration is a technique for numerical integration using random numbers. It is a particular method of Monte Carlo methods that numerically computes a definite integral. While other algorithms usually evaluate the integrand at a regular grid, Monte Carlo algorithms randomly choose the points at which the integrand is evaluated. This method is particularly useful for higher dimensional integrals.
Informally, to estimate the area of a domain D, first pick a simple domain E whose area is easily calculated and which contains D. Now pick a sequence of random points that fall within E. Some fraction of these points will also fall within D. The area of D is then estimated as this fraction multiplied by the area of E.
Particular techniques to perform a Monte Carlo integration can be considered. Uniform sampling, stratified sampling and importance sampling are the most common.
Read more about Monte Carlo Integration: Overview, Recursive Stratified Sampling
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