手法を比較

	階層ベイズ推論	階層マルコフ連鎖モンテカルロ法
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1972 (Lindley & Smith); consolidated 1995–2013	1990
提唱者	Lindley & Smith; Gelman et al.	Gelfand & Smith (1990), building on Geman & Geman (1984)
種類	Bayesian multilevel model	Bayesian computational 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	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	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model	hierarchical MCMC, MCMC for multilevel models, Bayesian hierarchical MCMC, multilevel MCMC sampling
関連	6	6
概要	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.	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.