Methoden vergleichen

	MCMC bei fehlenden Daten	Bayessches hierarchisches Modell
Fachgebiet	Bayes-Statistik	Bayes-Statistik
Familie	Bayesian methods	Bayesian methods
Entstehungsjahr	1987	2006
Urheber	Tanner & Wong (data augmentation); extended by Gelfand & Smith, Rubin	Gelman & Hill (2006); Bayesian multilevel tradition
Typ	Bayesian computational method	hierarchical probabilistic model
Wegweisende Quelle	Little, R. J. A. & Rubin, D. B. (2002). Statistical Analysis with Missing Data (2nd ed.). Wiley. ISBN: 978-0471183860	Gelman, A. & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
Aliasnamen	MCMC missing data, data augmentation MCMC, Bayesian multiple imputation, MCMC imputation	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model
Verwandt	6	4
Zusammenfassung	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.	Bayesian hierarchical modelling, popularised by Gelman and Hill (2006), is a Bayesian approach to nested data structures — such as students within schools within districts — that estimates separate parameters at each level while allowing those levels to share statistical strength through a mechanism called partial pooling. Where a classical hierarchical linear model treats group means as fixed unknown quantities, the Bayesian version places hyperprior distributions on those group means so that information flows freely across levels, producing more reliable group-level estimates whenever any individual group has few observations.