Linganisha mbinu

	Hamiltonian Monte Carlo wa Ngazi Nyingi	Hamiltonian Monte Carlo (HMC) ya Ngazi
Nyanja	Mbinu za Bayes	Mbinu za Bayes
Familia	Bayesian methods	Bayesian methods
Mwaka wa asili	2010s	2015
Mwanzilishi	Beskos, Jasra, Law, Tempone, Zhou (multilevel MCMC); Neal (HMC component)	Betancourt & Girolami
Aina	Bayesian computational sampler	Bayesian sampling algorithm
Chanzo asilia	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.
Majina mbadala	Multilevel HMC, MLHMC, multilevel HMC sampler, multilevel leapfrog MCMC	Hierarchical HMC, HMC for hierarchical models, HMC with reparameterization, NUTS for hierarchical Bayesian models
Zinazohusiana	5	5
Muhtasari	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.