مقایسهٔ روش‌ها

	زنجیره مارکوف مونت کارلوی سلسله‌مراتبی	الگوریتم متروپولیس-هستینگز
حوزه	بیزی	بیزی
خانواده	Bayesian methods	Bayesian methods
سال پیدایش	1990	1953
پدیدآور	Gelfand & Smith (1990), building on Geman & Geman (1984)	Metropolis et al. (1953); generalised by Hastings (1970)
نوع	Bayesian computational sampler	Markov chain Monte Carlo sampler
منبع بنیادین	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955	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.
نام‌های دیگر	hierarchical MCMC, MCMC for multilevel models, Bayesian hierarchical MCMC, multilevel MCMC sampling	MH algorithm, M-H algorithm, Metropolis algorithm, Metropolis-Hastings sampler
مرتبط	6	5
خلاصه	Hierarchical Markov chain Monte Carlo applies MCMC sampling to hierarchical Bayesian models, jointly drawing from the posterior over both observation-level parameters and the hyperparameters that govern them. This allows principled uncertainty propagation across all levels of a multilevel structure, from individuals to groups to population, using algorithms such as Gibbs sampling, Metropolis-Hastings, or Hamiltonian Monte Carlo.	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.