Katana VentraIP

Monte Carlo integration

In mathematics, Monte Carlo integration is a technique for numerical integration using random numbers. It is a particular Monte Carlo method that numerically computes a definite integral. While other algorithms usually evaluate the integrand at a regular grid,[1] Monte Carlo randomly chooses points at which the integrand is evaluated.[2] This method is particularly useful for higher-dimensional integrals.[3]

There are different methods to perform a Monte Carlo integration, such as uniform sampling, stratified sampling, importance sampling, sequential Monte Carlo (also known as a particle filter), and mean-field particle methods.

Quasi-Monte Carlo method

Auxiliary field Monte Carlo

Monte Carlo method in statistical physics

Monte Carlo method

Variance reduction

 : A blog article describing Monte Carlo integration (principle, hypothesis, confidence interval)

Café math : Monte Carlo Integration

Boost.Math : Naive Monte Carlo integration: Documentation for the C++ naive Monte-Carlo routines

Monte Carlo applet applied in statistical physics problems