Сравнение на методи

	Многостепенен Хамилтонов Монте Карло	Йерархичен Монте Карло на Хамилтон
Област	Бейсови методи	Бейсови методи
Семейство	Bayesian methods	Bayesian methods
Година на възникване	2010s	2015
Създател	Beskos, Jasra, Law, Tempone, Zhou (multilevel MCMC); Neal (HMC component)	Betancourt & Girolami
Тип	Bayesian computational sampler	Bayesian sampling algorithm
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.	Betancourt, M. & Girolami, M. (2015). Hamiltonian Monte Carlo for hierarchical models. In S. K. Upadhyay, U. Singh, D. K. Dey & A. Loganathan (Eds.), Current Trends in Bayesian Methodology with Applications (pp. 79-101). CRC Press.
Други названия	Multilevel HMC, MLHMC, multilevel HMC sampler, multilevel leapfrog MCMC	Hierarchical HMC, HMC for hierarchical models, HMC with reparameterization, NUTS for hierarchical Bayesian models
Свързани	5	5
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.	Hierarchical Hamiltonian Monte Carlo (Hierarchical HMC) applies Hamiltonian Monte Carlo sampling to Bayesian hierarchical models, addressing the severe geometric challenges those models pose. By combining non-centered parameterizations with HMC's gradient-driven proposals, it achieves efficient posterior exploration of the multi-level funnel-shaped geometries that standard MCMC methods struggle with.