قارن الطرق

	نموذج بايزي هرمي مع بيانات مفقودة	الاستمثال البايزي المتسلسل مع البيانات المفقودة
المجال	بايزي	بايزي
العائلة	Bayesian methods	Bayesian methods
سنة النشأة	1990s–2000s	1987
صاحب الطريقة	Gelman, Rubin, Little (and collaborators)	Tanner & Wong (data augmentation); extended by Gelfand & Smith, Rubin
النوع	Bayesian hierarchical model with missing-data integration	Bayesian computational method
المصدر التأسيسي	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
الأسماء البديلة	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
ذات صلة	5	6
الملخص	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.