手法を比較

	欠損値を含むベイズ推論	Gibbs Sampling
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1976–1987	1984
提唱者	Rubin, D. B. (missing-data mechanisms); Tanner & Wong (data augmentation)	Stuart Geman & Donald Geman
種類	Bayesian probabilistic model	MCMC sampling algorithm
原典	Little, R. J. A. & Rubin, D. B. (2002). Statistical Analysis with Missing Data (2nd ed.). Wiley-Interscience. 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	Bayesian missing data analysis, Bayesian data augmentation, Bayesian imputation, missing data Bayesian model	Gibbs sampler, coordinate-wise MCMC, systematic scan Gibbs, blocked Gibbs sampling
関連	6	5
概要	Bayesian inference with missing data treats unobserved values as unknown parameters and integrates them out of the posterior distribution. Rather than deleting or ad hoc imputing incomplete records, the method jointly models observed and missing data under an explicit missing-data mechanism, producing fully calibrated posterior uncertainty that honestly reflects what the data cannot tell us.	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.