手法を比較

	ベイズ回帰	混合効果モデル	リッジ回帰
分野	ベイズ	統計学	機械学習
系統	Bayesian methods	Regression model	Machine learning
提唱年	—	1982	1970
提唱者	—	Laird & Ware	Hoerl, A.E. & Kennard, R.W.
種類	Bayesian linear model	Mixed effects regression	L2-regularized linear regression
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	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.
別名	bayesian linear regression, probabilistic regression, bayesian regresyon	LME, LMM, mixed model, random effects model	Ridge Regresyonu, ridge regresyonu, L2-regularized regression, Tikhonov regularization
関連	2	4	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.	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.