手法を比較

	欠損データを含む変分推論	欠損値を含むMCMC (MCMC with missing data)
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1994–2008	1987
提唱者	Ghahramani & Jordan; Wainwright & Jordan (formal foundations)	Tanner & Wong (data augmentation); extended by Gelfand & Smith, Rubin
種類	Approximate Bayesian inference	Bayesian computational method
原典	Ghahramani, Z. & Jordan, M. I. (1994). Supervised learning from incomplete data via an EM approach. In Cowan, J. D., Tesauro, G. & Alspector, J. (Eds.), Advances in Neural Information Processing Systems 6 (pp. 120–127). Morgan Kaufmann.	Little, R. J. A. & Rubin, D. B. (2002). Statistical Analysis with Missing Data (2nd ed.). Wiley. ISBN: 978-0471183860
別名	VI with missing data, variational EM with missing data, VB missing data, mean-field VI for incomplete data	MCMC missing data, data augmentation MCMC, Bayesian multiple imputation, MCMC imputation
関連	4	6
概要	Variational inference with missing data is a scalable Bayesian approach that simultaneously approximates the posterior over latent variables and model parameters while imputing missing observations. Instead of integrating over all possible values of the missing entries exactly, it posits a tractable approximate distribution and optimises it to be as close as possible to the true joint posterior, yielding fast, principled inference even in high-dimensional incomplete datasets.	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.