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	गिब्स सैंपलिंग	बेयसियन रिग्रेशन	पदानुक्रमिक बायेसियन अनुमान
क्षेत्र	बायेसियन	बायेसियन	बायेसियन
परिवार	Bayesian methods	Bayesian methods	Bayesian methods
उद्भव वर्ष	1984	—	1972 (Lindley & Smith); consolidated 1995–2013
प्रवर्तक	Stuart Geman & Donald Geman	—	Lindley & Smith; Gelman et al.
प्रकार	MCMC sampling algorithm	Bayesian linear model	Bayesian multilevel model
मौलिक स्रोत	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	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
उपनाम	Gibbs sampler, coordinate-wise MCMC, systematic scan Gibbs, blocked Gibbs sampling	bayesian linear regression, probabilistic regression, bayesian regresyon	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model
संबंधित	5	2	6
सारांश	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.	Bayesian regression is a probabilistic version of linear regression that treats the model parameters as uncertain quantities. Instead of returning a single best-fit estimate, it combines prior knowledge with the observed data to produce a full posterior probability distribution for each parameter, from which credible intervals and predictions are read off.	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.