Comparer des méthodes

	Hamiltonien de Monte Carlo multiniveau	Inférence variationnelle multiniveau
Domaine	Bayésien	Bayésien
Famille	Bayesian methods	Bayesian methods
Année d'origine	2010s	2016
Auteur d'origine	Beskos, Jasra, Law, Tempone, Zhou (multilevel MCMC); Neal (HMC component)	Ranganath, Altosaar, Tran, Blei (hierarchical VI formalization, 2016); Blei et al. (VI framework, 2017)
Type	Bayesian computational sampler	approximate Bayesian inference
Source fondatrice	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.
Alias	Multilevel HMC, MLHMC, multilevel HMC sampler, multilevel leapfrog MCMC	hierarchical variational inference, multilevel VI, variational Bayes for multilevel models, MLVI
Apparentées	5	4
Résumé	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.