Comparer des méthodes

	Algorithme de Metropolis-Hastings	Échantillonnage de Gibbs
Domaine	Bayésien	Bayésien
Famille	Bayesian methods	Bayesian methods
Année d'origine	1953	1984
Auteur d'origine	Metropolis et al. (1953); generalised by Hastings (1970)	Stuart Geman & Donald Geman
Type	Markov chain Monte Carlo sampler	MCMC sampling algorithm
Source fondatrice	Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953). Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 21(6), 1087–1092.	Geman, S. & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6), 721-741.
Alias	MH algorithm, M-H algorithm, Metropolis algorithm, Metropolis-Hastings sampler	Gibbs sampler, coordinate-wise MCMC, systematic scan Gibbs, blocked Gibbs sampling
Apparentées	5	5
Résumé	The Metropolis-Hastings (MH) algorithm is a general-purpose Markov chain Monte Carlo (MCMC) method for drawing samples from any probability distribution whose density can be evaluated up to a normalising constant. Introduced by Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller (1953) in computational physics and generalised by Hastings (1970) to asymmetric proposal distributions, it is the foundational algorithm from which nearly all subsequent MCMC samplers — Gibbs sampling, Hamiltonian Monte Carlo, slice sampling — are derived or can be viewed as special cases.	Gibbs sampling is a Markov chain Monte Carlo algorithm that approximates a high-dimensional posterior distribution by repeatedly drawing each parameter from its full conditional distribution given all other parameters and the data. Because each draw is exact from a conditional — not a proposal that may be rejected — the sampler is efficient when those conditionals are available in closed form.