方法对比

	多层哈密顿蒙特卡洛 (Multilevel Hamiltonian Monte Carlo)	马尔可夫链蒙特卡洛 (MCMC)
领域	贝叶斯	仿真
方法族	Bayesian methods	Process / pipeline
起源年份	2010s	1953 (Metropolis-Hastings); 1984 (Gibbs)
提出者	Beskos, Jasra, Law, Tempone, Zhou (multilevel MCMC); Neal (HMC component)	Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984)
类型	Bayesian computational sampler	Simulation-based Bayesian inference / numerical integration
开创性文献	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.
别名	Multilevel HMC, MLHMC, multilevel HMC sampler, multilevel leapfrog MCMC	MCMC, Metropolis-Hastings, Gibbs sampling, Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs)
相关	5	5
摘要	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.