方法对比

	经验贝叶斯	马尔可夫链蒙特卡洛 (MCMC)	混合效应模型	岭回归（Ridge Regression）
领域	贝叶斯	贝叶斯	统计学	机器学习
方法族	Bayesian methods	Bayesian methods	Regression model	Machine learning
起源年份	—	—	1982	1970
提出者	Herbert Robbins (1956); Bradley Efron & Carl Morris (1973)	—	Laird & Ware	Hoerl, A.E. & Kennard, R.W.
类型	Empirical Bayes estimator	Posterior sampling algorithm	Mixed effects regression	L2-regularized linear regression
开创性文献	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.	Hoerl, A.E. & Kennard, R.W. (1970). Ridge Regression: Biased Estimation for Nonorthogonal Problems. Technometrics, 12(1), 55–67.
别名	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	Ridge Regresyonu, ridge regresyonu, L2-regularized regression, Tikhonov regularization
相关	4	3	4	4
摘要	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.	Ridge Regression is an L2-regularized linear regression method, introduced by Arthur Hoerl and Robert Kennard in 1970, that reduces multicollinearity by adding a penalty on the size of the coefficients. It shrinks coefficients toward zero without setting any of them exactly to zero, producing more stable estimates when predictors are highly correlated.