手法を比較

	欠損データを含む逐次モンテカルロ法	欠損値を有するギブスサンプリング
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1993–2001	1987–1990
提唱者	Gordon, Salmond & Smith (particle filter, 1993); missing-data extensions formalised by Doucet et al. (2000s)	Tanner & Wong (data augmentation), Gelfand & Smith (Gibbs sampler)
種類	Sequential Bayesian filtering / smoothing	Bayesian computational method
原典	Doucet, A., de Freitas, N., & Gordon, N. (Eds.) (2001). Sequential Monte Carlo Methods in Practice. Springer, New York. ISBN: 978-0387951461	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.
別名	SMC with missing data, particle filter with missing observations, SMC missing observations, particle smoothing with incomplete data	data augmentation Gibbs sampler, Gibbs sampler with data augmentation, Bayesian imputation via Gibbs sampling, MCMC missing data imputation
関連	6	6
概要	Sequential Monte Carlo (SMC) with missing data extends the standard particle filter to state-space models in which some observations are absent. When an observation is missing at a given time step the update step is simply skipped: particles are propagated forward through the transition model without reweighting, preserving exact Bayesian inference under any missing-data pattern as long as missingness is ignorable (missing at random or missing completely at random).	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.