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	Multilevel Hamiltonian Monte Carlo	階層的ハミルトニアン・モンテカルロ法
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	2010s	2015
提唱者	Beskos, Jasra, Law, Tempone, Zhou (multilevel MCMC); Neal (HMC component)	Betancourt & Girolami
種類	Bayesian computational sampler	Bayesian sampling algorithm
原典	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.	Betancourt, M. & Girolami, M. (2015). Hamiltonian Monte Carlo for hierarchical models. In S. K. Upadhyay, U. Singh, D. K. Dey & A. Loganathan (Eds.), Current Trends in Bayesian Methodology with Applications (pp. 79-101). CRC Press.
別名	Multilevel HMC, MLHMC, multilevel HMC sampler, multilevel leapfrog MCMC	Hierarchical HMC, HMC for hierarchical models, HMC with reparameterization, NUTS for hierarchical Bayesian models
関連	5	5
概要	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.	Hierarchical Hamiltonian Monte Carlo (Hierarchical HMC) applies Hamiltonian Monte Carlo sampling to Bayesian hierarchical models, addressing the severe geometric challenges those models pose. By combining non-centered parameterizations with HMC's gradient-driven proposals, it achieves efficient posterior exploration of the multi-level funnel-shaped geometries that standard MCMC methods struggle with.