Linganisha mbinu

	Utafsiri wa Kibayes wa Kienyeji	Markov Chain Monte Carlo (MCMC) ya Tabaka
Nyanja	Mbinu za Bayes	Mbinu za Bayes
Familia	Bayesian methods	Bayesian methods
Mwaka wa asili	1972 (Lindley & Smith); consolidated 1995–2013	1990
Mwanzilishi	Lindley & Smith; Gelman et al.	Gelfand & Smith (1990), building on Geman & Geman (1984)
Aina	Bayesian multilevel model	Bayesian computational sampler
Chanzo asilia	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
Majina mbadala	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model	hierarchical MCMC, MCMC for multilevel models, Bayesian hierarchical MCMC, multilevel MCMC sampling
Zinazohusiana	6	6
Muhtasari	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.