قارن الطرق

	ميتروبوليس-هاستينغز مع البيانات المفقودة	أخذ العينات بجيبس مع البيانات المفقودة
المجال	بايزي	بايزي
العائلة	Bayesian methods	Bayesian methods
سنة النشأة	1953 / 1987	1987–1990
صاحب الطريقة	Metropolis et al. (1953); missing-data extension formalised by Tanner & Wong (1987)	Tanner & Wong (data augmentation), Gelfand & Smith (Gibbs sampler)
النوع	MCMC sampler with latent-variable augmentation	Bayesian computational method
المصدر التأسيسي	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.
الأسماء البديلة	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
ذات صلة	6	6
الملخص	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.