So sánh phương pháp

	Hamiltonian Monte Carlo Đa cấp	Suy diễn biến phân đa cấp
Lĩnh vực	Bayes	Bayes
Họ	Bayesian methods	Bayesian methods
Năm ra đời	2010s	2016
Người khởi xướng	Beskos, Jasra, Law, Tempone, Zhou (multilevel MCMC); Neal (HMC component)	Ranganath, Altosaar, Tran, Blei (hierarchical VI formalization, 2016); Blei et al. (VI framework, 2017)
Loại	Bayesian computational sampler	approximate Bayesian inference
Công trình gốc	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.
Tên gọi khác	Multilevel HMC, MLHMC, multilevel HMC sampler, multilevel leapfrog MCMC	hierarchical variational inference, multilevel VI, variational Bayes for multilevel models, MLVI
Liên quan	5	4
Tóm tắt	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.