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	Multilevel Variational Inference	マルチレベルMCMC
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	2016	1990s
提唱者	Ranganath, Altosaar, Tran, Blei (hierarchical VI formalization, 2016); Blei et al. (VI framework, 2017)	Gelfand & Smith (sampling-based approach); multilevel extension developed through 1990s Bayesian hierarchical modeling literature
種類	approximate Bayesian inference	Bayesian computational inference
原典	Blei, D. M., Kucukelbir, A., & McAuliffe, J. D. (2017). Variational inference: A review for statisticians. Journal of the American Statistical Association, 112(518), 859-877.	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955
別名	hierarchical variational inference, multilevel VI, variational Bayes for multilevel models, MLVI	hierarchical MCMC, multilevel Bayesian sampling, MLMCMC, hierarchical Markov chain Monte Carlo
関連	4	6
概要	Multilevel variational inference (MLVI) is a scalable approximate Bayesian method that fits hierarchical (multilevel) models by optimizing a variational approximation to the posterior, rather than drawing MCMC samples. It exploits the grouped structure of multilevel data — individuals nested within groups, groups nested within higher-level units — to derive efficient coordinate-wise updates, making Bayesian inference tractable for large clustered datasets.	Multilevel MCMC applies Markov chain Monte Carlo sampling to hierarchical (multilevel) Bayesian models. It draws samples from the joint posterior of both group-level and population-level parameters simultaneously, propagating uncertainty across levels and enabling inference in clustered or nested data structures where observations within groups share common distributional characteristics.