Сравнение на методи

	Многостепенен Хамилтонов Монте Карло	Многостепенен вариационен извод
Област	Бейсови методи	Бейсови методи
Семейство	Bayesian methods	Bayesian methods
Година на възникване	2010s	2016
Създател	Beskos, Jasra, Law, Tempone, Zhou (multilevel MCMC); Neal (HMC component)	Ranganath, Altosaar, Tran, Blei (hierarchical VI formalization, 2016); Blei et al. (VI framework, 2017)
Тип	Bayesian computational sampler	approximate Bayesian inference
Основополагащ източник	Beskos, A., Jasra, A., Law, K., Tempone, R., & Zhou, Y. (2017). Multilevel sequential Monte Carlo samplers. Stochastic Processes and their Applications, 127(5), 1417–1440.	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.
Други названия	Multilevel HMC, MLHMC, multilevel HMC sampler, multilevel leapfrog MCMC	hierarchical variational inference, multilevel VI, variational Bayes for multilevel models, MLVI
Свързани	5	4
Резюме	Multilevel Hamiltonian Monte Carlo (Multilevel HMC) combines the variance-reduction strategy of multilevel Monte Carlo with the efficient gradient-driven exploration of Hamiltonian Monte Carlo. By running coupled HMC chains at increasing levels of model fidelity or discretisation, it achieves accurate posterior estimates at a computational cost substantially lower than a single fine-level HMC chain.	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.