手法を比較

	多層ギブスサンプリング	ベイズ階層モデル
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1990	2006
提唱者	Geman & Geman (1984); applied to multilevel models by Gelfand & Smith (1990)	Gelman & Hill (2006); Bayesian multilevel tradition
種類	MCMC sampling algorithm	hierarchical probabilistic model
原典	Gelman, A. & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891	Gelman, A. & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
別名	hierarchical Gibbs sampler, blocked Gibbs sampling for multilevel models, multilevel MCMC via Gibbs, Gibbs sampler for mixed-effects models	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model
関連	6	4
概要	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.	Bayesian hierarchical modelling, popularised by Gelman and Hill (2006), is a Bayesian approach to nested data structures — such as students within schools within districts — that estimates separate parameters at each level while allowing those levels to share statistical strength through a mechanism called partial pooling. Where a classical hierarchical linear model treats group means as fixed unknown quantities, the Bayesian version places hyperprior distributions on those group means so that information flows freely across levels, producing more reliable group-level estimates whenever any individual group has few observations.