Linganisha mbinu

	Utaftaji wa Bayesian wenye Data Zilizokosekana	Modeli wa Mfumo wa Kihierarkia wa Bayesian Wenye Data Zilizokosekana
Nyanja	Mbinu za Bayes	Mbinu za Bayes
Familia	Bayesian methods	Bayesian methods
Mwaka wa asili	1976–1987	1990s–2000s
Mwanzilishi	Rubin, D. B. (missing-data mechanisms); Tanner & Wong (data augmentation)	Gelman, Rubin, Little (and collaborators)
Aina	Bayesian probabilistic model	Bayesian hierarchical model with missing-data integration
Chanzo asilia	Little, R. J. A. & Rubin, D. B. (2002). Statistical Analysis with Missing Data (2nd ed.). Wiley-Interscience. ISBN: 978-0471183860	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
Majina mbadala	Bayesian missing data analysis, Bayesian data augmentation, Bayesian imputation, missing data Bayesian model	BHM missing data, multilevel Bayesian missing data model, hierarchical Bayesian imputation, Bayesian multilevel model with incomplete data
Zinazohusiana	6	5
Muhtasari	Bayesian inference with missing data treats unobserved values as unknown parameters and integrates them out of the posterior distribution. Rather than deleting or ad hoc imputing incomplete records, the method jointly models observed and missing data under an explicit missing-data mechanism, producing fully calibrated posterior uncertainty that honestly reflects what the data cannot tell us.	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.