手法を比較

	ハミルトニアンモンテカルロ	階層ベイズ推論
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1987	1972 (Lindley & Smith); consolidated 1995–2013
提唱者	—	Lindley & Smith; Gelman et al.
種類	Gradient-based Markov chain Monte Carlo sampler	Bayesian multilevel model
原典	Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195(2), 216–222.	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	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model
関連	3	6
概要	Hamiltonian Monte Carlo (HMC) is a gradient-based Markov chain Monte Carlo algorithm that uses the geometry of the log-posterior surface to make large, informed jumps through parameter space instead of the small random steps of classical MCMC. Originally introduced for lattice field theory by Duane, Kennedy, Pendleton, and Roweth (1987) under the name Hybrid Monte Carlo, and brought into mainstream statistics by Radford Neal's authoritative 2011 chapter, HMC is today the default sampler in Stan and PyMC and is widely regarded as the state-of-the-art engine for Bayesian posterior inference in high-dimensional models.	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.