Metropolis–Hastings algorithm

Summary

The Metropolis–Hastings algorithm is a Markov chain Monte Carlo method. It turns an arbitrary proposal mechanism into a Markov chain with a prescribed stationary distribution $\pi$. At each step a candidate move is proposed and then accepted or rejected with a probability chosen to enforce detailed balance. Only ratios $\pi(y)/\pi(x)$ enter, so the normalising constant of $\pi$ is never needed.