পদ্ধতির তুলনা করুন

	মাল্টিলেভেল হ্যামিলটোনিয়ান মন্টি কার্লো	হায়ারারকিক্যাল হ্যামিল্টোনিয়ান মন্টে কার্লো
ক্ষেত্র	বেইসীয়	বেইসীয়
পরিবার	Bayesian methods	Bayesian methods
উদ্ভবের বছর	2010s	2015
প্রবর্তক	Beskos, Jasra, Law, Tempone, Zhou (multilevel MCMC); Neal (HMC component)	Betancourt & Girolami
ধরন	Bayesian computational sampler	Bayesian sampling algorithm
মৌলিক উৎস	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.
অপর নাম	Multilevel HMC, MLHMC, multilevel HMC sampler, multilevel leapfrog MCMC	Hierarchical HMC, HMC for hierarchical models, HMC with reparameterization, NUTS for hierarchical Bayesian models
সম্পর্কিত	5	5
সারসংক্ষেপ	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.