Monte Carlo Method
- Variants of the Monte Carlo method:
- Direct simulation Monte Carlo
- Quasi-Monte Carlo method
- Markov chain Monte Carlo
- Metropolis–Hastings algorithm
- Multiple-try Metropolis — modification which allows larger step sizes
- Wang and Landau algorithm — extension of Metropolis Monte Carlo
- Equation of State Calculations by Fast Computing Machines — 1953 article proposing the Metropolis Monte Carlo algorithm
- Gibbs sampling
- Coupling from the past
- Reversible-jump Markov chain Monte Carlo
- Metropolis–Hastings algorithm
- Dynamic Monte Carlo method
- Kinetic Monte Carlo
- Gillespie algorithm
- Particle filter
- Auxiliary particle filter
- Reverse Monte Carlo
- Demon algorithm
- Pseudo-random number sampling
- Inverse transform sampling — general and straightforward method but computationally expensive
- Rejection sampling — sample from a simpler distribution but reject some of the samples
- Ziggurat algorithm — uses a pre-computed table covering the probability distribution with rectangular segments
- For sampling from a normal distribution:
- Box–Muller transform
- Marsaglia polar method
- Convolution random number generator — generates a random variable as a sum of other random variables
- Indexed search
- Variance reduction techniques:
- Antithetic variates
- Control variates
- Importance sampling
- Stratified sampling
- VEGAS algorithm
- Low-discrepancy sequence
- Constructions of low-discrepancy sequences
- Event generator
- Parallel tempering
- Umbrella sampling — improves sampling in physical systems with significant energy barriers
- Hybrid Monte Carlo
- Ensemble Kalman filter — recursive filter suitable for problems with a large number of variables
- Transition path sampling
- Applications:
- Ensemble forecasting — produce multiple numerical predictions from slightly initial conditions or parameters
- Bond fluctuation model — for simulating the conformation and dynamics of polymer systems
- Iterated filtering
- Metropolis light transport
- Monte Carlo methods for electron transport
- Monte Carlo method for photon transport
- Monte Carlo methods in finance
- Monte Carlo methods for option pricing
- Quasi-Monte Carlo methods in finance
- Monte Carlo molecular modeling
- Path integral molecular dynamics — incorporates Feynman path integrals
- Quantum Monte Carlo
- Diffusion Monte Carlo — uses a Green function to solve the Schrödinger equation
- Gaussian quantum Monte Carlo
- Path integral Monte Carlo
- Reptation Monte Carlo
- Variational Monte Carlo
- Methods for simulating the Ising model:
- Swendsen–Wang algorithm — entire sample is divided into equal-spin clusters
- Wolff algorithm — improvement of the Swendsen–Wang algorithm
- Metropolis–Hastings algorithm
- Auxiliary field Monte Carlo — computes averages of operators in many-body quantum mechanical problems
- Cross-entropy method — for multi-extremal optimization and importance sampling
- Also see the list of statistics topics
Read more about this topic: List Of Numerical Analysis Topics
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