قارن الطرق

	الاستدلال البايزي مع البيانات المفقودة	نموذج بايزي هرمي مع بيانات مفقودة
المجال	بايزي	بايزي
العائلة	Bayesian methods	Bayesian methods
سنة النشأة	1976–1987	1990s–2000s
صاحب الطريقة	Rubin, D. B. (missing-data mechanisms); Tanner & Wong (data augmentation)	Gelman, Rubin, Little (and collaborators)
النوع	Bayesian probabilistic model	Bayesian hierarchical model with missing-data integration
المصدر التأسيسي	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
الأسماء البديلة	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
ذات صلة	6	5
الملخص	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.