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| 다층 메트로폴리스-헤이스팅스× | 다수준 변분 추론× | |
|---|---|---|
| 분야 | 베이지안 | 베이지안 |
| 계열 | Bayesian methods | Bayesian methods |
| 기원 연도≠ | 1953 (core); 1990s (multilevel application) | 2016 |
| 창시자≠ | Metropolis et al. (1953); hierarchical extension developed through 1980s–1990s Bayesian computation literature | Ranganath, Altosaar, Tran, Blei (hierarchical VI formalization, 2016); Blei et al. (VI framework, 2017) |
| 유형≠ | MCMC sampling algorithm | approximate Bayesian inference |
| 원전≠ | Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955 | 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 ↗ |
| 별칭 | hierarchical Metropolis-Hastings, multilevel MH, MH for hierarchical models, blocked Metropolis-Hastings | hierarchical variational inference, multilevel VI, variational Bayes for multilevel models, MLVI |
| 관련≠ | 6 | 4 |
| 요약≠ | Multilevel Metropolis-Hastings applies the Metropolis-Hastings MCMC algorithm to hierarchical (multilevel) Bayesian models, sampling jointly from group-level parameters and hyperparameters by proposing candidate values and accepting or rejecting them via a ratio that respects the full joint posterior across all levels of the model. | 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. |
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