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	Bayesian Multiple linear regression	最小二乗法 (OLS) 回帰
分野	統計学	計量経済学
系統	Regression model	Regression model
提唱年	1971	2019
提唱者	Arnold Zellner (econometric formulation); broader development by Harold Jeffreys and Gelman et al.	Wooldridge (textbook treatment); classical least squares
種類	Bayesian parametric regression	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	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860
別名	Bayesian MLR, Bayesian linear regression, Bayesian multivariate regression, conjugate normal-inverse-gamma regression	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu
関連	6	5
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.	Ordinary Least Squares is the classical linear regression method that explains a continuous outcome as a linear combination of predictors. It estimates the coefficients by minimising the sum of squared residuals, and under the Gauss-Markov assumptions these estimates are the best linear unbiased estimator (BLUE).