手法を比較

	階層的ハミルトニアン・モンテカルロ法	階層ベイズ推論
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	2015	1972 (Lindley & Smith); consolidated 1995–2013
提唱者	Betancourt & Girolami	Lindley & Smith; Gelman et al.
種類	Bayesian sampling algorithm	Bayesian multilevel model
原典	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
別名	Hierarchical HMC, HMC for hierarchical models, HMC with reparameterization, NUTS for hierarchical Bayesian models	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model
関連	5	6
概要	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 Bayesian inference is a probabilistic modeling framework that organises parameters into levels, placing priors on the group-level parameters and hyperpriors on the parameters governing those priors. It enables partial pooling of information across groups, balancing the extremes of treating each group as independent or merging them into a single estimate.