手法を比較

	階層的変分推論	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	2016	1990
提唱者	Ranganath, Altosaar, Tran & Blei	Gelfand & Smith (1990), building on Geman & Geman (1984)
種類	Bayesian approximate inference	Bayesian computational sampler
原典	Ranganath, R., Altosaar, J., Tran, D. & Blei, D. M. (2016). Hierarchical Variational Models. Proceedings of the 33rd International Conference on Machine Learning (ICML 2016), PMLR 48, 324-333.	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	HVI, hierarchical variational models, hierarchical VI, hierarchical approximate inference	hierarchical MCMC, MCMC for multilevel models, Bayesian hierarchical MCMC, multilevel MCMC sampling
関連	5	6
概要	Hierarchical variational inference (HVI) extends standard variational inference by placing a richer, hierarchical structure on the variational family itself. Instead of using a simple mean-field approximation, HVI introduces auxiliary latent variables that capture dependencies among the main latent variables, yielding tighter evidence lower bounds and more accurate posterior approximations for complex Bayesian models.	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.