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	Bayesian Multiple linear regression	リッジ回帰
分野	統計学	機械学習
系統	Regression model	Machine learning
提唱年	1971	1970
提唱者	Arnold Zellner (econometric formulation); broader development by Harold Jeffreys and Gelman et al.	Hoerl, A.E. & Kennard, R.W.
種類	Bayesian parametric 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	Hoerl, A.E. & Kennard, R.W. (1970). Ridge Regression: Biased Estimation for Nonorthogonal Problems. Technometrics, 12(1), 55–67.
別名	Bayesian MLR, Bayesian linear regression, Bayesian multivariate regression, conjugate normal-inverse-gamma regression	Ridge Regresyonu, ridge regresyonu, L2-regularized regression, Tikhonov regularization
関連	6	4
概要	Bayesian Multiple Linear Regression models a continuous outcome as a linear combination of several predictors, but instead of producing a single point estimate it yields a full posterior distribution over all regression coefficients and the error variance. This makes uncertainty quantification explicit and allows seamlessly incorporating prior knowledge from theory or previous studies.	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.