Monte Carlo method

A family of computational methods that use random sampling to estimate numerical results or solve problems that are difficult to handle exactly. Their accuracy is assessed statistically and generally improves with more samples.

Monte Carlo integration: A numerical integration technique that estimates an integral by averaging function values at randomly sampled points. It turns integration over complex domains into an average of sampled values.
Particle transport simulation: A computational model of how particles move and interact with matter or fields. Randomly sampled interactions estimate transport when tracking every possible particle history is impractical.
Stanislaw Ulam: A Polish-American mathematician who contributed to nuclear physics, computing, and the development of the hydrogen bomb. Ulam proposed using random sampling to estimate probabilities in neutron diffusion problems.
Probability distribution: A mathematical description of the possible values of a random variable and their probabilities. A Monte Carlo procedure must specify or construct the distribution from which it samples.
Numerical integration: The approximation of definite integrals using finite computational procedures. Monte Carlo integration is one approach within this broader family of methods.
Law of large numbers: A theorem stating that sample averages converge toward expected values as the number of independent observations grows. It explains why estimates based on random samples stabilize with more trials.
Radiative transfer: The propagation of radiation through a medium, including absorption, emission, and scattering. Monte Carlo simulations handle complex scattering paths in atmospheric and astrophysical media.
John von Neumann: A Hungarian-American mathematician whose work helped shape modern computing, game theory, and mathematical physics. He helped develop and promote the sampling approach for problems in nuclear physics.
Random number generation: The production of numerical sequences intended to behave like draws from a specified probability distribution. Sampling algorithms depend on generated values that represent the desired randomness.
Deterministic algorithm: An algorithm whose next operation is fixed by its input and current state, without random choices. Monte Carlo algorithms deliberately use random choices, unlike deterministic procedures.

Linked from 84 pages