Markov chain Monte Carlo

Summary

Markov chain Monte Carlo (MCMC) is a family of methods to sample from a probability distribution $\pi$. They run a Markov chain whose stationary distribution is $\pi$. Averages of a function along the path of the chain then estimate the expectation of that function under $\pi$. MCMC works even when $\pi$ is known only up to a normalising constant, which makes it a basic tool of Bayesian statistics and statistical physics. The Metropolis–Hastings algorithm and the Gibbs sampler are the main examples.