Linganisha mbinu

	Modeli wa Mfumo wa Kihierarkia wa Bayesian Wenye Data Zilizokosekana	MCMC yenye Data Zilizokosekana
Nyanja	Mbinu za Bayes	Mbinu za Bayes
Familia	Bayesian methods	Bayesian methods
Mwaka wa asili	1990s–2000s	1987
Mwanzilishi	Gelman, Rubin, Little (and collaborators)	Tanner & Wong (data augmentation); extended by Gelfand & Smith, Rubin
Aina	Bayesian hierarchical model with missing-data integration	Bayesian computational method
Chanzo asilia	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	Little, R. J. A. & Rubin, D. B. (2002). Statistical Analysis with Missing Data (2nd ed.). Wiley. ISBN: 978-0471183860
Majina mbadala	BHM missing data, multilevel Bayesian missing data model, hierarchical Bayesian imputation, Bayesian multilevel model with incomplete data	MCMC missing data, data augmentation MCMC, Bayesian multiple imputation, MCMC imputation
Zinazohusiana	5	6
Muhtasari	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.	MCMC with missing data is a Bayesian computational strategy that treats unobserved values as additional unknown parameters. By alternating between sampling the missing values from their predictive distribution and sampling the model parameters from their posterior, the algorithm produces a valid joint posterior that fully accounts for uncertainty introduced by the missingness.