قارن الطرق

	تحليل الأسبقية المترافقة	باِيز التجريبي	سلاسل ماركوف مونت كارلو (MCMC)
المجال	بايزي	بايزي	بايزي
العائلة	Bayesian methods	Bayesian methods	Bayesian methods
سنة النشأة	1961	—	—
صاحب الطريقة	Raiffa & Schlaifer (1961); DeGroot (1970)	Herbert Robbins (1956); Bradley Efron & Carl Morris (1973)	—
النوع	Closed-form Bayesian model	Empirical Bayes estimator	Posterior sampling algorithm
المصدر التأسيسي	Raiffa, H. & Schlaifer, R. (1961). Applied Statistical Decision Theory. Harvard University Press. ISBN: 978-0-87584-017-8	Robbins, H. (1956). An empirical Bayes approach to statistics. In J. Neyman (Ed.), Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1 (pp. 157–164). University of California Press.	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
الأسماء البديلة	conjugate priors, conjugate Bayesian updating, closed-form posterior analysis, Beta-Binomial model	EB, empirical Bayes estimation, marginal likelihood estimation, James-Stein shrinkage	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
ذات صلة	3	4	3
الملخص	Conjugate prior analysis is a class of Bayesian inference methods in which the prior distribution and the likelihood belong to a matched family — called a conjugate pair — so that the posterior distribution has exactly the same functional form as the prior and can be derived in closed form. Introduced systematically by Raiffa and Schlaifer (1961) and consolidated by DeGroot (1970), conjugate analysis is the pedagogic backbone of introductory Bayesian statistics and a practical tool whenever analytical tractability is required.	Empirical Bayes (EB) is an estimation strategy, introduced by Herbert Robbins in 1956 and developed into practical shrinkage estimators by Bradley Efron and Carl Morris in 1973, in which the hyperparameters of the prior distribution are estimated from the observed data via the marginal likelihood rather than specified in advance. The resulting posterior retains a Bayesian structure but substitutes data-driven hyperparameters for subjective ones, bridging frequentist shrinkage and full Bayesian inference.	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.