Võrdle meetodeid

	Mitmetasemeline variatsiooniline järeldamine	Bayesian Hierarchical Model
Valdkond	Bayesi meetodid	Bayesi meetodid
Perekond	Bayesian methods	Bayesian methods
Tekkeaasta	2016	2006
Looja	Ranganath, Altosaar, Tran, Blei (hierarchical VI formalization, 2016); Blei et al. (VI framework, 2017)	Gelman & Hill (2006); Bayesian multilevel tradition
Tüüp	approximate Bayesian inference	hierarchical probabilistic model
Algallikas	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. & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
Rööpnimetused	hierarchical variational inference, multilevel VI, variational Bayes for multilevel models, MLVI	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model
Seotud	4	4
Kokkuvõte	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.	Bayesian hierarchical modelling, popularised by Gelman and Hill (2006), is a Bayesian approach to nested data structures — such as students within schools within districts — that estimates separate parameters at each level while allowing those levels to share statistical strength through a mechanism called partial pooling. Where a classical hierarchical linear model treats group means as fixed unknown quantities, the Bayesian version places hyperprior distributions on those group means so that information flows freely across levels, producing more reliable group-level estimates whenever any individual group has few observations.