مقایسهٔ روش‌ها

	بایز تجربی	زنجیره مارکوف مونت کارلو (MCMC)	مدل اثرات مختلط (یا مدل خطی مختلط) رگرسیون معمولی را با گنجاندن هر دو اثرات ثابت
حوزه	بیزی	بیزی	آمار
خانواده	Bayesian methods	Bayesian methods	Regression model
سال پیدایش	—	—	1982
پدیدآور	Herbert Robbins (1956); Bradley Efron & Carl Morris (1973)	—	Laird & Ware
نوع	Empirical Bayes estimator	Posterior sampling algorithm	Mixed effects regression
منبع بنیادین	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	Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38(4), 963–974.
نام‌های دیگر	EB, empirical Bayes estimation, marginal likelihood estimation, James-Stein shrinkage	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)	LME, LMM, mixed model, random effects model
مرتبط	4	3	4
خلاصه	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.	A mixed effects model (or linear mixed model) extends ordinary regression by including both fixed effects — population-level parameters shared by all observations — and random effects that capture subject-, group-, or cluster-level variability. It is the standard tool for repeated-measures, longitudinal, and multilevel data where observations within the same unit are correlated.