方法对比

	多层自助法模拟	多层变分推断
领域	贝叶斯	贝叶斯
方法族	Bayesian methods	Bayesian methods
起源年份	1979 (bootstrap); multilevel variants c.1990s	2016
提出者	Efron (1979); multilevel extensions developed through 1980s–2000s	Ranganath, Altosaar, Tran, Blei (hierarchical VI formalization, 2016); Blei et al. (VI framework, 2017)
类型	resampling / simulation	approximate Bayesian inference
开创性文献	Efron, B. (1979). Bootstrap methods: Another look at the jackknife. The Annals of Statistics, 7(1), 1–26.	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.
别名	hierarchical bootstrap, cluster bootstrap, stratified bootstrap for multilevel data, multilevel resampling	hierarchical variational inference, multilevel VI, variational Bayes for multilevel models, MLVI
相关	6	4
摘要	Multilevel bootstrap simulation is a resampling technique designed for clustered or hierarchically structured data. It preserves the nested data structure by resampling at each level independently — first drawing clusters (e.g., schools, hospitals), then drawing observations within each sampled cluster — so that bootstrap replicate datasets reflect the same multilevel organisation as the original data.	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.