مقایسهٔ روش‌ها

	متروپلیس-هستینگز چندسطحی	همیلتونین مونت کارلو چندسطحی
حوزه	بیزی	بیزی
خانواده	Bayesian methods	Bayesian methods
سال پیدایش	1953 (core); 1990s (multilevel application)	2010s
پدیدآور	Metropolis et al. (1953); hierarchical extension developed through 1980s–1990s Bayesian computation literature	Beskos, Jasra, Law, Tempone, Zhou (multilevel MCMC); Neal (HMC component)
نوع	MCMC sampling algorithm	Bayesian computational sampler
منبع بنیادین	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955	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.
نام‌های دیگر	hierarchical Metropolis-Hastings, multilevel MH, MH for hierarchical models, blocked Metropolis-Hastings	Multilevel HMC, MLHMC, multilevel HMC sampler, multilevel leapfrog MCMC
مرتبط	6	5
خلاصه	Multilevel Metropolis-Hastings applies the Metropolis-Hastings MCMC algorithm to hierarchical (multilevel) Bayesian models, sampling jointly from group-level parameters and hyperparameters by proposing candidate values and accepting or rejecting them via a ratio that respects the full joint posterior across all levels of the model.	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.