Monte Carlo method

Monte Carlo methods, also called Monte Carlo experiments or simulations, are a broad class of computational algorithms that obtain numerical results by repeated random sampling. The underlying idea is to use randomness to solve deterministic problems, and the approach was conceptualized by the Polish mathematician Stanislaw Ulam, and the name comes from the Monte Carlo Casino in Monaco. They are mainly used for three classes of problem: optimization, numerical integration and generating draws from a probability distribution, and they suit systems with significant input uncertainty, such as risk assessments for nuclear power plants. Most follow one pattern: define a domain of possible inputs, generate inputs randomly from a probability distribution over it, perform a deterministic computation on each input and aggregate the results. Estimating pi by scattering points over a square that contains a quarter circle is the standard illustration, and the estimate improves as more points are used, provided they are uniformly distributed.