Σύγκριση μεθόδων

	Metropolis-Hastings με Ελλείποντα Δεδομένα	Δειγματοληψία Gibbs με Ελλιπή Δεδομένα
Πεδίο	Μπεϋζιανή Στατιστική	Μπεϋζιανή Στατιστική
Οικογένεια	Bayesian methods	Bayesian methods
Έτος προέλευσης	1953 / 1987	1987–1990
Δημιουργός	Metropolis et al. (1953); missing-data extension formalised by Tanner & Wong (1987)	Tanner & Wong (data augmentation), Gelfand & Smith (Gibbs sampler)
Τύπος	MCMC sampler with latent-variable augmentation	Bayesian computational method
Θεμελιώδης πηγή	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.	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.
Εναλλακτικές ονομασίες	MH with missing data, Metropolis-Hastings data augmentation, MCMC missing data imputation, MH data-augmentation sampler	data augmentation Gibbs sampler, Gibbs sampler with data augmentation, Bayesian imputation via Gibbs sampling, MCMC missing data imputation
Συναφείς	6	6
Σύνοψη	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.	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.