So sánh phương pháp

	Hamiltonian Monte Carlo Đa cấp	Multilevel MCMC
Lĩnh vực	Bayes	Bayes
Họ	Bayesian methods	Bayesian methods
Năm ra đời	2010s	1990s
Người khởi xướng	Beskos, Jasra, Law, Tempone, Zhou (multilevel MCMC); Neal (HMC component)	Gelfand & Smith (sampling-based approach); multilevel extension developed through 1990s Bayesian hierarchical modeling literature
Loại	Bayesian computational sampler	Bayesian computational 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.	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
Tên gọi khác	Multilevel HMC, MLHMC, multilevel HMC sampler, multilevel leapfrog MCMC	hierarchical MCMC, multilevel Bayesian sampling, MLMCMC, hierarchical Markov chain Monte Carlo
Liên quan	5	6
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 MCMC applies Markov chain Monte Carlo sampling to hierarchical (multilevel) Bayesian models. It draws samples from the joint posterior of both group-level and population-level parameters simultaneously, propagating uncertainty across levels and enabling inference in clustered or nested data structures where observations within groups share common distributional characteristics.