Порівняння методів

	Ієрархічний ланцюг Маркова Монте-Карло	Ієрархічний байєсівський висновок
Галузь	Баєсові методи	Баєсові методи
Родина	Bayesian methods	Bayesian methods
Рік появи	1990	1972 (Lindley & Smith); consolidated 1995–2013
Автор методу	Gelfand & Smith (1990), building on Geman & Geman (1984)	Lindley & Smith; Gelman et al.
Тип	Bayesian computational sampler	Bayesian multilevel model
Основоположне джерело	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
Інші назви	hierarchical MCMC, MCMC for multilevel models, Bayesian hierarchical MCMC, multilevel MCMC sampling	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model
Пов'язані	6	6
Підсумок	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.	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.