Methoden vergleichen

	Gibbs-Sampling	Hierarchische Bayes'sche Inferenz
Fachgebiet	Bayes-Statistik	Bayes-Statistik
Familie	Bayesian methods	Bayesian methods
Entstehungsjahr	1984	1972 (Lindley & Smith); consolidated 1995–2013
Urheber	Stuart Geman & Donald Geman	Lindley & Smith; Gelman et al.
Typ	MCMC sampling algorithm	Bayesian multilevel model
Wegweisende Quelle	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.	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
Aliasnamen	Gibbs sampler, coordinate-wise MCMC, systematic scan Gibbs, blocked Gibbs sampling	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model
Verwandt	5	6
Zusammenfassung	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.	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.