Сравнение на методи

	Многостепенно семплиране на Гибс	Алгоритъм на Метрополис-Хастингс
Област	Бейсови методи	Бейсови методи
Семейство	Bayesian methods	Bayesian methods
Година на възникване	1990	1953
Създател	Geman & Geman (1984); applied to multilevel models by Gelfand & Smith (1990)	Metropolis et al. (1953); generalised by Hastings (1970)
Тип	MCMC sampling algorithm	Markov chain Monte Carlo sampler
Основополагащ източник	Gelman, A. & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891	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.
Други названия	hierarchical Gibbs sampler, blocked Gibbs sampling for multilevel models, multilevel MCMC via Gibbs, Gibbs sampler for mixed-effects models	MH algorithm, M-H algorithm, Metropolis algorithm, Metropolis-Hastings sampler
Свързани	6	5
Резюме	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.	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.