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	Multilevel Bayesian Network	階層ベイズ推論
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1990s–2000s	1980s–2000s
提唱者	Extension of Pearl's Bayesian networks; multilevel formulation developed in statistical relational learning community, 1990s–2000s	Gelman, Hill, Raudenbush, Bryk
種類	Probabilistic graphical model (hierarchical)	Bayesian hierarchical model
原典	Koller, D. & Friedman, N. (2009). Probabilistic Graphical Models: Principles and Techniques. MIT Press. ISBN: 978-0262013192	Gelman, A., & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891
別名	multi-level Bayesian network, hierarchical Bayesian network, MLBN, multilevel probabilistic graphical model	Bayesian multilevel model, Bayesian hierarchical model, Bayesian mixed-effects model, Bayesian random-effects model
関連	6	6
概要	A multilevel Bayesian network extends the standard Bayesian network to data with hierarchical or grouped structure — students within schools, patients within hospitals, observations within subjects — by placing separate but linked graphical models at each level, with higher-level parameters governing the conditional probability tables of lower-level nodes. The result is a principled probabilistic framework that captures both within-group relationships and between-group variation.	Multilevel Bayesian inference combines Bayesian probability with hierarchical data structures, treating group-level parameters as drawn from a common population distribution. It simultaneously estimates unit-level effects and the hyperparameters governing their variation, propagating full uncertainty through every level of the hierarchy via posterior sampling.