Metropolis-adjusted Langevin algorithm

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. As the name suggests, MALA uses a combination of two mechanisms to generate the states of a random walk that has the target probability distribution as an invariant measure: new states are proposed using (overdamped) Langevin dynamics, which use evaluations of the gradient of the target probability density function; these proposals are accepted or rejected using the Metropolis–Hastings algorithm, which uses evaluations of the target probability density (but not its gradient).

Source: Wikipedia — Metropolis-adjusted Langevin algorithm (CC BY-SA 4.0)