قارن الطرق

	الاستمثال البايزي المتسلسل مع البيانات المفقودة	النموذج الهرمي البيزي
المجال	بايزي	بايزي
العائلة	Bayesian methods	Bayesian methods
سنة النشأة	1987	2006
صاحب الطريقة	Tanner & Wong (data augmentation); extended by Gelfand & Smith, Rubin	Gelman & Hill (2006); Bayesian multilevel tradition
النوع	Bayesian computational method	hierarchical probabilistic model
المصدر التأسيسي	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.
الأسماء البديلة	MCMC missing data, data augmentation MCMC, Bayesian multiple imputation, MCMC imputation	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model
ذات صلة	6	4
الملخص	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.