方法对比

	带缺失数据的吉布斯抽样	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	1987–1990	1990s–2000s
提出者	Tanner & Wong (data augmentation), Gelfand & Smith (Gibbs sampler)	Gelman, Rubin, Little (and collaborators)
类型	Bayesian computational method	Bayesian hierarchical model with missing-data integration
开创性文献	Tanner, M. A. & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association, 82(398), 528–540.	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	data augmentation Gibbs sampler, Gibbs sampler with data augmentation, Bayesian imputation via Gibbs sampling, MCMC missing data imputation	BHM missing data, multilevel Bayesian missing data model, hierarchical Bayesian imputation, Bayesian multilevel model with incomplete data
相关	6	5
摘要	Gibbs sampling with missing data treats unobserved values as additional unknowns alongside model parameters and samples all of them jointly within a Markov chain Monte Carlo loop. The method alternates between drawing the missing values from their conditional distribution given the parameters and drawing the parameters from their conditional distribution given the completed data, producing a posterior over both simultaneously.	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.