手法を比較

	多層ギブスサンプリング	階層ベイズ推論
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1990	1972 (Lindley & Smith); consolidated 1995–2013
提唱者	Geman & Geman (1984); applied to multilevel models by Gelfand & Smith (1990)	Lindley & Smith; Gelman et al.
種類	MCMC sampling algorithm	Bayesian multilevel model
原典	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
別名	hierarchical Gibbs sampler, blocked Gibbs sampling for multilevel models, multilevel MCMC via Gibbs, Gibbs sampler for mixed-effects models	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model
関連	6	6
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.	Hierarchical Bayesian inference is a probabilistic modeling framework that organises parameters into levels, placing priors on the group-level parameters and hyperpriors on the parameters governing those priors. It enables partial pooling of information across groups, balancing the extremes of treating each group as independent or merging them into a single estimate.