Σύγκριση μεθόδων

	Πολυεπίπεδη Metropolis-Hastings	Δειγματοληψία Gibbs Πολλαπλών Επιπέδων
Πεδίο	Μπεϋζιανή Στατιστική	Μπεϋζιανή Στατιστική
Οικογένεια	Bayesian methods	Bayesian methods
Έτος προέλευσης	1953 (core); 1990s (multilevel application)	1990
Δημιουργός	Metropolis et al. (1953); hierarchical extension developed through 1980s–1990s Bayesian computation literature	Geman & Geman (1984); applied to multilevel models by Gelfand & Smith (1990)
Τύπος	MCMC sampling algorithm	MCMC sampling algorithm
Θεμελιώδης πηγή	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	Gelman, A. & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891
Εναλλακτικές ονομασίες	hierarchical Metropolis-Hastings, multilevel MH, MH for hierarchical models, blocked Metropolis-Hastings	hierarchical Gibbs sampler, blocked Gibbs sampling for multilevel models, multilevel MCMC via Gibbs, Gibbs sampler for mixed-effects models
Συναφείς	6	6
Σύνοψη	Multilevel Metropolis-Hastings applies the Metropolis-Hastings MCMC algorithm to hierarchical (multilevel) Bayesian models, sampling jointly from group-level parameters and hyperparameters by proposing candidate values and accepting or rejecting them via a ratio that respects the full joint posterior across all levels of the model.	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.