השוואת שיטות

	המילטוניאן מונטה קרלו רב-רמתי	Markov Chain Monte Carlo (MCMC)
תחום	בייסיאני	סימולציה
משפחה	Bayesian methods	Process / pipeline
שנת המקור	2010s	1953 (Metropolis-Hastings); 1984 (Gibbs)
הוגה השיטה	Beskos, Jasra, Law, Tempone, Zhou (multilevel MCMC); Neal (HMC component)	Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984)
סוג	Bayesian computational sampler	Simulation-based Bayesian inference / numerical integration
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.	Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A. & Rubin, D.B. (2013). Bayesian Data Analysis (3rd ed.). Chapman & Hall/CRC.
כינויים	Multilevel HMC, MLHMC, multilevel HMC sampler, multilevel leapfrog MCMC	MCMC, Metropolis-Hastings, Gibbs sampling, Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs)
קשורות	5	5
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.	Markov Chain Monte Carlo (MCMC) is a family of simulation algorithms that constructs a Markov chain whose stationary distribution is the target posterior, enabling Bayesian inference and high-dimensional integral computation that would otherwise be analytically intractable. Pioneered by Metropolis and colleagues in 1953 and extended by Hastings in 1970, MCMC underpins modern Bayesian statistics. The two most widely used variants are Metropolis-Hastings, which proposes moves from a general proposal distribution, and Gibbs sampling, which draws each parameter in turn from its full conditional distribution.