方法对比

	多层贝叶斯网络	含缺失数据的贝叶斯分层模型
领域	贝叶斯	贝叶斯
方法族	Bayesian methods	Bayesian methods
起源年份	1990s–2000s	1990s–2000s
提出者	Extension of Pearl's Bayesian networks; multilevel formulation developed in statistical relational learning community, 1990s–2000s	Gelman, Rubin, Little (and collaborators)
类型	Probabilistic graphical model (hierarchical)	Bayesian hierarchical model with missing-data integration
开创性文献	Koller, D. & Friedman, N. (2009). Probabilistic Graphical Models: Principles and Techniques. MIT Press. ISBN: 978-0262013192	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
别名	multi-level Bayesian network, hierarchical Bayesian network, MLBN, multilevel probabilistic graphical model	BHM missing data, multilevel Bayesian missing data model, hierarchical Bayesian imputation, Bayesian multilevel model with incomplete data
相关	6	5
摘要	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.	A Bayesian hierarchical model with missing data treats unobserved values as additional unknowns and samples them jointly with all model parameters from the posterior. The nested structure of the hierarchy borrows strength across groups, while the Bayesian framework naturally propagates uncertainty from missingness through every estimate and prediction.