مقایسهٔ روش‌ها

	میانگین‌گیری بیزی چندسطحی	استنتاج بایزی سطوح متعدد
حوزه	بیزی	بیزی
خانواده	Bayesian methods	Bayesian methods
سال پیدایش	1999–2000s	2016
پدیدآور	Hoeting, Madigan, Raftery, Volinsky (BMA foundation); multilevel extension developed across the late 1990s–2000s	Ranganath, Altosaar, Tran, Blei (hierarchical VI formalization, 2016); Blei et al. (VI framework, 2017)
نوع	Bayesian ensemble / model selection	approximate Bayesian inference
منبع بنیادین	Hoeting, J. A., Madigan, D., Raftery, A. E. & Volinsky, C. T. (1999). Bayesian model averaging: A tutorial. Statistical Science, 14(4), 382-401.	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.
نام‌های دیگر	ML-BMA, hierarchical Bayesian model averaging, multilevel BMA, Bayesian model averaging in multilevel models	hierarchical variational inference, multilevel VI, variational Bayes for multilevel models, MLVI
مرتبط	6	4
خلاصه	Multilevel Bayesian model averaging (ML-BMA) extends classical Bayesian model averaging to grouped or hierarchically structured data. Rather than committing to a single multilevel model specification, it computes a weighted average of predictions and parameter estimates across a set of candidate multilevel models, weighting each model by its posterior probability given the data. The result accounts simultaneously for uncertainty in the grouping structure, fixed effects, random effects, and covariate selection.	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.