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	Metropolis-Hastings z brakującymi danymi	Uzupełnianie wielokrotne
Dziedzina	Statystyka bayesowska	Statystyka
Rodzina	Bayesian methods	Process / pipeline
Rok powstania	1953 / 1987	1987
Twórca	Metropolis et al. (1953); missing-data extension formalised by Tanner & Wong (1987)	Donald B. Rubin
Typ	MCMC sampler with latent-variable augmentation	Missing-data handling procedure
Źródło pierwotne	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.	Rubin, D.B. (1987). Multiple Imputation for Nonresponse in Surveys. Wiley.
Inne nazwy	MH with missing data, Metropolis-Hastings data augmentation, MCMC missing data imputation, MH data-augmentation sampler	MICE, Multivariate Imputation by Chained Equations, Çoklu Atama (Multiple Imputation — MICE)
Pokrewne	6	1
Podsumowanie	Metropolis-Hastings with missing data treats unobserved values as latent variables and samples them jointly with model parameters inside a single MCMC chain. By augmenting the target distribution to include both parameters and missing values, the algorithm yields properly calibrated posterior inference without discarding incomplete cases or requiring a separate imputation step.	Multiple Imputation (MI), formally introduced by Donald B. Rubin in 1987, is a principled statistical procedure for handling missing data. Rather than replacing each missing value once, MI fills the gaps m times — each time drawing plausible values from the posterior predictive distribution of the missing data — producing m complete datasets. Each dataset is analysed independently, and the results are combined into a single set of estimates using Rubin's pooling rules. The MICE variant (Multivariate Imputation by Chained Equations), popularised by van Buuren and Groothuis-Oudshoorn (2011), extends the approach to mixed variable types by imputing each variable in turn through a sequence of conditional regression models.