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	ベイズ頑健回帰	Bayesian Multiple linear regression
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	1993	1971
提唱者	Geweke (1993); Gelman et al. (2013)	Arnold Zellner (econometric formulation); broader development by Harold Jeffreys and Gelman et al.
種類	Bayesian regression with heavy-tailed errors	Bayesian parametric regression
原典	Geweke, J. (1993). Bayesian treatment of the independent Student-t linear model. Journal of Applied Econometrics, 8(S1), S19–S40.	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 heavy-tailed regression, Bayesian Student-t regression, robust Bayesian linear model, BRR	Bayesian MLR, Bayesian linear regression, Bayesian multivariate regression, conjugate normal-inverse-gamma regression
関連	6	6
概要	Bayesian Robust Regression replaces the Gaussian error assumption of ordinary linear regression with a heavy-tailed distribution — most commonly the Student-t — and estimates all parameters in a Bayesian framework. The heavier tails give outliers less influence on the fitted line, yielding stable coefficient estimates and honest uncertainty intervals even when the data contain unusual observations.	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.