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In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution.Given a probability distribution, one can construct a Markov chain whose elements' distribution approximates it – that is, the Markov chain's equilibrium distribution matches the target distribution.
The Metropolis-Hastings algorithm sampling a normal one-dimensional posterior probability distribution.. In statistics and statistical physics, the Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution from which direct sampling is difficult.
In computational statistics, the Metropolis-adjusted Langevin algorithm (MALA) or Langevin Monte Carlo (LMC) is a Markov chain Monte Carlo (MCMC) method for obtaining random samples – sequences of random observations – from a probability distribution for which direct sampling is difficult.
In the 1930s, Enrico Fermi first experimented with the Monte Carlo method while studying neutron diffusion, but he did not publish this work. [19] In the late 1940s, Stanisław Ulam invented the modern version of the Markov Chain Monte Carlo method while he was working on nuclear weapons projects at the Los Alamos National Laboratory.
Hamiltonian Monte Carlo sampling a two-dimensional probability distribution. The Hamiltonian Monte Carlo algorithm (originally known as hybrid Monte Carlo) is a Markov chain Monte Carlo method for obtaining a sequence of random samples whose distribution converges to a target probability distribution that is difficult
Among Markov chain Monte Carlo (MCMC) algorithms, coupling from the past is a method for sampling from the stationary distribution of a Markov chain. Contrary to many MCMC algorithms, coupling from the past gives in principle a perfect sample from the stationary distribution. It was invented by James Propp and David Wilson in 1996.
Therefore, Markov Chain Monte Carlo method can be used to draw samples randomly from a black-box to approximate the probability distribution of attributes over a range of objects. [ 67 ] Markov chains are used in lattice QCD simulations.
Two examples of such algorithms are the Karger–Stein algorithm [1] and the Monte Carlo algorithm for minimum feedback arc set. [2] The name refers to the Monte Carlo casino in the Principality of Monaco, which is well-known around the world as an icon of gambling. The term "Monte Carlo" was first introduced in 1947 by Nicholas Metropolis. [3]