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	Bayesian Multiple linear regression	ベイズ線形回帰（単純）
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	1971	Early 19th century; textbook synthesis 2013
提唱者	Arnold Zellner (econometric formulation); broader development by Harold Jeffreys and Gelman et al.	Laplace, P.-S. (early 19th c.); modern treatment: Gelman et al.
種類	Bayesian parametric regression	Bayesian 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	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
別名	Bayesian MLR, Bayesian linear regression, Bayesian multivariate regression, conjugate normal-inverse-gamma regression	Bayesian SLR, Bayesian univariate regression, probabilistic simple linear regression, Bayesian linear model
関連	6	6
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.	Bayesian Simple Linear Regression models the relationship between a continuous outcome and a single predictor by combining a Gaussian likelihood with prior distributions over the intercept, slope, and error variance. The result is a full posterior distribution over all parameters, providing probabilistic uncertainty quantification rather than a single point estimate.