Linganisha mbinu

	Utafiti wa Kiwango cha Juu wa Utabiri	Markov Chain Monte Carlo (MCMC) ya Tabaka
Nyanja	Mbinu za Bayes	Mbinu za Bayes
Familia	Bayesian methods	Bayesian methods
Mwaka wa asili	2016	1990
Mwanzilishi	Ranganath, Altosaar, Tran & Blei	Gelfand & Smith (1990), building on Geman & Geman (1984)
Aina	Bayesian approximate inference	Bayesian computational sampler
Chanzo asilia	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
Majina mbadala	HVI, hierarchical variational models, hierarchical VI, hierarchical approximate inference	hierarchical MCMC, MCMC for multilevel models, Bayesian hierarchical MCMC, multilevel MCMC sampling
Zinazohusiana	5	6
Muhtasari	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.