مقایسهٔ روش‌ها

	استنتاج بایزی سطوح متعدد	استنتاج بیزی سلسله‌مراتبی
حوزه	بیزی	بیزی
خانواده	Bayesian methods	Bayesian methods
سال پیدایش	2016	1972 (Lindley & Smith); consolidated 1995–2013
پدیدآور	Ranganath, Altosaar, Tran, Blei (hierarchical VI formalization, 2016); Blei et al. (VI framework, 2017)	Lindley & Smith; Gelman et al.
نوع	approximate Bayesian inference	Bayesian multilevel model
منبع بنیادین	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
نام‌های دیگر	hierarchical variational inference, multilevel VI, variational Bayes for multilevel models, MLVI	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model
مرتبط	4	6
خلاصه	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.	Hierarchical Bayesian inference is a probabilistic modeling framework that organises parameters into levels, placing priors on the group-level parameters and hyperpriors on the parameters governing those priors. It enables partial pooling of information across groups, balancing the extremes of treating each group as independent or merging them into a single estimate.