手法を比較

	欠損値を含むMCMC (MCMC with missing data)	Gibbs Sampling
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1987	1984
提唱者	Tanner & Wong (data augmentation); extended by Gelfand & Smith, Rubin	Stuart Geman & Donald Geman
種類	Bayesian computational method	MCMC sampling algorithm
原典	Little, R. J. A. & Rubin, D. B. (2002). Statistical Analysis with Missing Data (2nd ed.). Wiley. ISBN: 978-0471183860	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.
別名	MCMC missing data, data augmentation MCMC, Bayesian multiple imputation, MCMC imputation	Gibbs sampler, coordinate-wise MCMC, systematic scan Gibbs, blocked Gibbs sampling
関連	6	5
概要	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.	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.