 Metropolis–Hastings algorithm

The Metropolis–Hastings algorithm proposes $y$ from $q(x,\cdot )$ at state $x$ and accepts it with probabilityThis acceptance rule enforces detailed balance with the target density $\pi$.

The Metropolis–Hastings algorithm is a Markov Chain Monte Carlo (MCMC) method used for sampling from probability distributions that are difficult to sample from directly. It is particularly useful in situations where the distribution is defined up to a normalization constant, making it challenging to derive samples analytically.