قارن الطرق

	هاميلتون مونت كارلو الهرمي (Hierarchical HMC)	سلسلة ماركوف مونت كارلو الهرمية
المجال	بايزي	بايزي
العائلة	Bayesian methods	Bayesian methods
سنة النشأة	2015	1990
صاحب الطريقة	Betancourt & Girolami	Gelfand & Smith (1990), building on Geman & Geman (1984)
النوع	Bayesian sampling algorithm	Bayesian computational sampler
المصدر التأسيسي	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.	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
الأسماء البديلة	Hierarchical HMC, HMC for hierarchical models, HMC with reparameterization, NUTS for hierarchical Bayesian models	hierarchical MCMC, MCMC for multilevel models, Bayesian hierarchical MCMC, multilevel MCMC sampling
ذات صلة	5	6
الملخص	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.	Hierarchical Markov chain Monte Carlo applies MCMC sampling to hierarchical Bayesian models, jointly drawing from the posterior over both observation-level parameters and the hyperparameters that govern them. This allows principled uncertainty propagation across all levels of a multilevel structure, from individuals to groups to population, using algorithms such as Gibbs sampling, Metropolis-Hastings, or Hamiltonian Monte Carlo.