Linganisha mbinu

	Modeli wa Mfumo wa Kihierarkia wa Bayesian Wenye Data Zilizokosekana	Utafsiri wa Kibayes wa Kienyeji
Nyanja	Mbinu za Bayes	Mbinu za Bayes
Familia	Bayesian methods	Bayesian methods
Mwaka wa asili	1990s–2000s	1972 (Lindley & Smith); consolidated 1995–2013
Mwanzilishi	Gelman, Rubin, Little (and collaborators)	Lindley & Smith; Gelman et al.
Aina	Bayesian hierarchical model with missing-data integration	Bayesian multilevel model
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	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	BHM missing data, multilevel Bayesian missing data model, hierarchical Bayesian imputation, Bayesian multilevel model with incomplete data	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model
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.	Hierarchical Bayesian inference is a probabilistic modeling framework that organises parameters into levels, placing priors on the group-level parameters and hyperpriors on the parameters governing those priors. It enables partial pooling of information across groups, balancing the extremes of treating each group as independent or merging them into a single estimate.