Сравнение на методи

	Многостепенен Хамилтонов Монте Карло	Хамилтънов Монте Карло
Област	Бейсови методи	Бейсови методи
Семейство	Bayesian methods	Bayesian methods
Година на възникване	2010s	1987
Създател	Beskos, Jasra, Law, Tempone, Zhou (multilevel MCMC); Neal (HMC component)	—
Тип	Bayesian computational sampler	Gradient-based Markov chain Monte Carlo sampler
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.	Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195(2), 216–222.
Други названия	Multilevel HMC, MLHMC, multilevel HMC sampler, multilevel leapfrog MCMC	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler
Свързани	5	3
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.	Hamiltonian Monte Carlo (HMC) is a gradient-based Markov chain Monte Carlo algorithm that uses the geometry of the log-posterior surface to make large, informed jumps through parameter space instead of the small random steps of classical MCMC. Originally introduced for lattice field theory by Duane, Kennedy, Pendleton, and Roweth (1987) under the name Hybrid Monte Carlo, and brought into mainstream statistics by Radford Neal's authoritative 2011 chapter, HMC is today the default sampler in Stan and PyMC and is widely regarded as the state-of-the-art engine for Bayesian posterior inference in high-dimensional models.