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	मिसिंग डेटा के साथ बायेसियन पदानुक्रमित मॉडल	लापता डेटा के साथ बायेसियन अनुमान
क्षेत्र	बायेसियन	बायेसियन
परिवार	Bayesian methods	Bayesian methods
उद्भव वर्ष	1990s–2000s	1976–1987
प्रवर्तक	Gelman, Rubin, Little (and collaborators)	Rubin, D. B. (missing-data mechanisms); Tanner & Wong (data augmentation)
प्रकार	Bayesian hierarchical model with missing-data integration	Bayesian probabilistic model
मौलिक स्रोत	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-Interscience. ISBN: 978-0471183860
उपनाम	BHM missing data, multilevel Bayesian missing data model, hierarchical Bayesian imputation, Bayesian multilevel model with incomplete data	Bayesian missing data analysis, Bayesian data augmentation, Bayesian imputation, missing data Bayesian model
संबंधित	5	6
सारांश	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.	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.