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	ベイズ線形回帰（単純）	ベイズ頑健回帰
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	Early 19th century; textbook synthesis 2013	1993
提唱者	Laplace, P.-S. (early 19th c.); modern treatment: Gelman et al.	Geweke (1993); Gelman et al. (2013)
種類	Bayesian linear regression	Bayesian regression with heavy-tailed errors
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	Geweke, J. (1993). Bayesian treatment of the independent Student-t linear model. Journal of Applied Econometrics, 8(S1), S19–S40.
別名	Bayesian SLR, Bayesian univariate regression, probabilistic simple linear regression, Bayesian linear model	Bayesian heavy-tailed regression, Bayesian Student-t regression, robust Bayesian linear model, BRR
関連	6	6
概要	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.	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.