방법 비교

	다단계 해밀턴ian 몬테카를로	해밀토니안 몬테카를로
분야	베이지안	베이지안
계열	Bayesian methods	Bayesian methods
기원 연도	2010s	1987
창시자	Beskos, Jasra, Law, Tempone, Zhou (multilevel MCMC); Neal (HMC component)	—
유형	Bayesian computational sampler	Gradient-based Markov chain Monte Carlo sampler
원전	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.
별칭	Multilevel HMC, MLHMC, multilevel HMC sampler, multilevel leapfrog MCMC	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler
관련	5	3
요약	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.