השוואת שיטות

	המילטוניאן מונטה קרלו רב-רמתי	המילטוניאן מונטה קרלו
תחום	בייסיאני	בייסיאני
משפחה	Bayesian methods	Bayesian methods
שנת המקור	2010s	1987
הוגה השיטה	Beskos, Jasra, Law, Tempone, Zhou (multilevel MCMC); Neal (HMC component)	—
סוג	Bayesian computational sampler	Gradient-based Markov chain Monte Carlo sampler
מקור מכונן	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.
כינויים	Multilevel HMC, MLHMC, multilevel HMC sampler, multilevel leapfrog MCMC	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler
קשורות	5	3
תקציר	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.