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	Gibbs-sampling med saknade data	Gibbs sampling
Ämnesområde	Bayesiansk statistik	Bayesiansk statistik
Familj	Bayesian methods	Bayesian methods
Ursprungsår	1987–1990	1984
Upphovsperson	Tanner & Wong (data augmentation), Gelfand & Smith (Gibbs sampler)	Stuart Geman & Donald Geman
Typ	Bayesian computational method	MCMC sampling algorithm
Ursprungskälla	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.	Geman, S. & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6), 721-741.
Alias	data augmentation Gibbs sampler, Gibbs sampler with data augmentation, Bayesian imputation via Gibbs sampling, MCMC missing data imputation	Gibbs sampler, coordinate-wise MCMC, systematic scan Gibbs, blocked Gibbs sampling
Närliggande	6	5
Sammanfattning	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.	Gibbs sampling is a Markov chain Monte Carlo algorithm that approximates a high-dimensional posterior distribution by repeatedly drawing each parameter from its full conditional distribution given all other parameters and the data. Because each draw is exact from a conditional — not a proposal that may be rejected — the sampler is efficient when those conditionals are available in closed form.