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	Multilevel Gibbs Sampling	Multilevel MCMC
Ämnesområde	Bayesiansk statistik	Bayesiansk statistik
Familj	Bayesian methods	Bayesian methods
Ursprungsår	1990	1990s
Upphovsperson	Geman & Geman (1984); applied to multilevel models by Gelfand & Smith (1990)	Gelfand & Smith (sampling-based approach); multilevel extension developed through 1990s Bayesian hierarchical modeling literature
Typ	MCMC sampling algorithm	Bayesian computational inference
Ursprungskälla	Gelman, A. & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891	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
Alias	hierarchical Gibbs sampler, blocked Gibbs sampling for multilevel models, multilevel MCMC via Gibbs, Gibbs sampler for mixed-effects models	hierarchical MCMC, multilevel Bayesian sampling, MLMCMC, hierarchical Markov chain Monte Carlo
Närliggande	6	6
Sammanfattning	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.	Multilevel MCMC applies Markov chain Monte Carlo sampling to hierarchical (multilevel) Bayesian models. It draws samples from the joint posterior of both group-level and population-level parameters simultaneously, propagating uncertainty across levels and enabling inference in clustered or nested data structures where observations within groups share common distributional characteristics.