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| Multilevel Variational Inference× | Bayessches hierarchisches Modell× | |
|---|---|---|
| Fachgebiet | Bayes-Statistik | Bayes-Statistik |
| Familie | Bayesian methods | Bayesian methods |
| Entstehungsjahr≠ | 2016 | 2006 |
| Urheber≠ | Ranganath, Altosaar, Tran, Blei (hierarchical VI formalization, 2016); Blei et al. (VI framework, 2017) | Gelman & Hill (2006); Bayesian multilevel tradition |
| Typ≠ | approximate Bayesian inference | hierarchical probabilistic model |
| Wegweisende Quelle≠ | 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. DOI ↗ | Gelman, A. & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. DOI ↗ |
| Aliasnamen≠ | hierarchical variational inference, multilevel VI, variational Bayes for multilevel models, MLVI | multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model |
| Verwandt | 4 | 4 |
| Zusammenfassung≠ | 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. |
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