Comparer des méthodes

	Échantillonnage de Gibbs multiniveaux	Échantillonnage de Gibbs
Domaine	Bayésien	Bayésien
Famille	Bayesian methods	Bayesian methods
Année d'origine	1990	1984
Auteur d'origine	Geman & Geman (1984); applied to multilevel models by Gelfand & Smith (1990)	Stuart Geman & Donald Geman
Type	MCMC sampling algorithm	MCMC sampling algorithm
Source fondatrice	Gelman, A. & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891	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	hierarchical Gibbs sampler, blocked Gibbs sampling for multilevel models, multilevel MCMC via Gibbs, Gibbs sampler for mixed-effects models	Gibbs sampler, coordinate-wise MCMC, systematic scan Gibbs, blocked Gibbs sampling
Apparentées	6	5
Résumé	Multilevel Gibbs sampling applies the Gibbs MCMC algorithm to hierarchical (multilevel) Bayesian models, cycling through the conditional distributions of group-level parameters and population-level hyperparameters in turn. This exploits the conditional independence structure of the hierarchy to draw exact or near-exact samples from a posterior that would otherwise be analytically intractable.	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.