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| ベイズ線形回帰（単純）× | ベイズ一般化線形モデル× | |
|---|---|---|
| 分野 | 統計学 | 統計学 |
| 系統 | Regression model | Regression model |
| 提唱年≠ | Early 19th century; textbook synthesis 2013 | 1989 (GLM); 1995 (Bayesian BDA) |
| 提唱者≠ | Laplace, P.-S. (early 19th c.); modern treatment: Gelman et al. | McCullagh & Nelder (GLM framework); Bayesian treatment formalized by Gelman et al. |
| 種類≠ | Bayesian linear regression | Bayesian regression model |
| 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 SLR, Bayesian univariate regression, probabilistic simple linear regression, Bayesian linear model | Bayesian GLM, Bayesian GLIM, Bayesian generalized linear regression, Bayes GLM |
| 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. | A Bayesian Generalized Linear Model (Bayesian GLM) extends the classical GLM framework by placing prior distributions on the regression coefficients and updating them with data via Bayes' theorem. This yields a full posterior distribution over parameters rather than single point estimates, enabling richer uncertainty quantification and principled incorporation of prior knowledge for any exponential-family outcome. |
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