विधियों की तुलना करें

	गिब्स सैंपलिंग	पदानुक्रमिक बायेसियन अनुमान	मार्कोव चेन मोंटे कार्लो (MCMC)
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 multilevel model	Posterior sampling algorithm
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	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
संबंधित	5	6	3
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.	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.	Markov Chain Monte Carlo (MCMC) is a family of computational algorithms for sampling from complex probability distributions, most commonly the posterior distributions that arise in Bayesian inference. Rather than computing posteriors analytically — which is rarely possible for realistic models — MCMC constructs a Markov chain whose stationary distribution is the target posterior and draws dependent samples from it, enabling full probabilistic inference for virtually any model.