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	Modello Gerarchico Bayesiano con Dati Mancanti	Campionamento di Gibbs con dati mancanti
Campo	Bayesiano	Bayesiano
Famiglia	Bayesian methods	Bayesian methods
Anno di origine	1990s–2000s	1987–1990
Ideatore	Gelman, Rubin, Little (and collaborators)	Tanner & Wong (data augmentation), Gelfand & Smith (Gibbs sampler)
Tipo	Bayesian hierarchical model with missing-data integration	Bayesian computational method
Fonte seminale	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	Tanner, M. A. & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association, 82(398), 528–540.
Alias	BHM missing data, multilevel Bayesian missing data model, hierarchical Bayesian imputation, Bayesian multilevel model with incomplete data	data augmentation Gibbs sampler, Gibbs sampler with data augmentation, Bayesian imputation via Gibbs sampling, MCMC missing data imputation
Correlati	5	6
Sintesi	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.	Gibbs sampling with missing data treats unobserved values as additional unknowns alongside model parameters and samples all of them jointly within a Markov chain Monte Carlo loop. The method alternates between drawing the missing values from their conditional distribution given the parameters and drawing the parameters from their conditional distribution given the completed data, producing a posterior over both simultaneously.