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| Regressione Lineare Multipla Bayesiana× | Regressione Lineare Semplice Bayesiana× | |
|---|---|---|
| Campo | Statistica | Statistica |
| Famiglia | Regression model | Regression model |
| Anno di origine≠ | 1971 | Early 19th century; textbook synthesis 2013 |
| Ideatore≠ | Arnold Zellner (econometric formulation); broader development by Harold Jeffreys and Gelman et al. | Laplace, P.-S. (early 19th c.); modern treatment: Gelman et al. |
| Tipo≠ | Bayesian parametric regression | Bayesian linear regression |
| Fonte seminale | 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 |
| Alias | 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 |
| Correlati | 6 | 6 |
| Sintesi≠ | 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. |
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