手法を比較

	ベイズ回帰	経験ベイズ
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	—	—
提唱者	—	Herbert Robbins (1956); Bradley Efron & Carl Morris (1973)
種類	Bayesian linear model	Empirical Bayes estimator
原典	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	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.
別名	bayesian linear regression, probabilistic regression, bayesian regresyon	EB, empirical Bayes estimation, marginal likelihood estimation, James-Stein shrinkage
関連	2	4
概要	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.	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.