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	Hierarchical Markov Chain Monte Carlo	Próbkowanie Gibbsa
Dziedzina	Statystyka bayesowska	Statystyka bayesowska
Rodzina	Bayesian methods	Bayesian methods
Rok powstania	1990	1984
Twórca	Gelfand & Smith (1990), building on Geman & Geman (1984)	Stuart Geman & Donald Geman
Typ	Bayesian computational sampler	MCMC sampling algorithm
Źródło pierwotne	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	Geman, S. & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6), 721-741.
Inne nazwy	hierarchical MCMC, MCMC for multilevel models, Bayesian hierarchical MCMC, multilevel MCMC sampling	Gibbs sampler, coordinate-wise MCMC, systematic scan Gibbs, blocked Gibbs sampling
Pokrewne	6	5
Podsumowanie	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.	Gibbs sampling is a Markov chain Monte Carlo algorithm that approximates a high-dimensional posterior distribution by repeatedly drawing each parameter from its full conditional distribution given all other parameters and the data. Because each draw is exact from a conditional — not a proposal that may be rejected — the sampler is efficient when those conditionals are available in closed form.