手法を比較

	階層マルコフ連鎖モンテカルロ法	ハミルトニアンモンテカルロ
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1990	1987
提唱者	Gelfand & Smith (1990), building on Geman & Geman (1984)	—
種類	Bayesian computational sampler	Gradient-based Markov chain Monte Carlo sampler
原典	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	Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195(2), 216–222.
別名	hierarchical MCMC, MCMC for multilevel models, Bayesian hierarchical MCMC, multilevel MCMC sampling	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler
関連	6	3
概要	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.	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.