ما معنى Markov chain Monte Carlo, Metropolis–Hastings, Gibbs sampler؟

Markov chain Monte Carlo (MCMC) draws from a density $\pi$ known up to a constant by running a Markov chain whose stationary distribution is $\pi$. The Metropolis–Hastings algorithm proposes $y \sim q(\cdot \mid x)$ from the current state $x$ and accepts it with probability $\alpha(x, y) = \min\bigl(1, \frac{\pi(y)q(x \mid y)}{\pi(x)q(y \mid x)}\bigr)$, staying at $x$ otherwise; with a symmetric random-walk proposal the ratio is $\pi(y)/\pi(x)$. The Gibbs sampler updates one block of coordinates at a time by a draw from its conditional law given the others.