Editing Monte Carlo integration (section)

{{Short description|Numerical technique}}
[[Image:MonteCarloIntegrationCircle.svg|thumb|An illustration of Monte Carlo integration. In this example, the domain ''D'' is the inner circle and the domain E is the square. Because the square's area (4) can be easily calculated, the area of the circle (π*1.0<sup>2</sup>) can be estimated by the ratio (0.8) of the points inside the circle (40) to the total number of points (50), yielding an approximation for the circle's area of 4*0.8 = 3.2 ≈ π.]]

In [[mathematics]], '''Monte Carlo integration''' is a technique for [[numerical quadrature|numerical integration]] using [[pseudorandomness|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,<ref>{{harvnb|Press|Teukolsky|Vetterling|Flannery|2007|loc=Chap. 4}}</ref> Monte Carlo randomly chooses points at which the integrand is evaluated.<ref>{{harvnb|Press|Teukolsky|Vetterling|Flannery|2007|loc=Chap. 7}}</ref> This method is particularly useful for higher-dimensional integrals.<ref name=newman1999ch2/>

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