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| Bayesian Robust Regression× | Bayesian Multiple Linear Regression× | |
|---|---|---|
| Fachgebiet | Statistik | Statistik |
| Familie | Regression model | Regression model |
| Entstehungsjahr≠ | 1993 | 1971 |
| Urheber≠ | Geweke (1993); Gelman et al. (2013) | Arnold Zellner (econometric formulation); broader development by Harold Jeffreys and Gelman et al. |
| Typ≠ | Bayesian regression with heavy-tailed errors | Bayesian parametric regression |
| Wegweisende Quelle≠ | Geweke, J. (1993). Bayesian treatment of the independent Student-t linear model. Journal of Applied Econometrics, 8(S1), S19–S40. DOI ↗ | 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 |
| Aliasnamen | 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 |
| Verwandt | 6 | 6 |
| Zusammenfassung≠ | 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. |
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