Linganisha mbinu

	Ulinganifu wa wastani wa modeli za kibayazilishi zenye viwango vingi	Uchanganuzi wa Kiwango-Nyingi wa Dhana
Nyanja	Mbinu za Bayes	Mbinu za Bayes
Familia	Bayesian methods	Bayesian methods
Mwaka wa asili	1999–2000s	2016
Mwanzilishi	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)
Aina	Bayesian ensemble / model selection	approximate Bayesian inference
Chanzo asilia	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.
Majina mbadala	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
Zinazohusiana	6	4
Muhtasari	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.