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| Bayesiansk Tobitmodell× | Bayesiansk multipel linjär regression× | |
|---|---|---|
| Ämnesområde | Statistik | Statistik |
| Familj | Regression model | Regression model |
| Ursprungsår≠ | 1958 (classical); 1992 (Bayesian formulation) | 1971 |
| Upphovsperson≠ | James Tobin (classical Tobit, 1958); Siddhartha Chib (Bayesian Tobit, 1992) | Arnold Zellner (econometric formulation); broader development by Harold Jeffreys and Gelman et al. |
| Typ≠ | Bayesian censored/limited-dependent-variable regression | Bayesian parametric regression |
| Ursprungskälla≠ | Tobin, J. (1958). Estimation of relationships for limited dependent variables. Econometrica, 26(1), 24–36. 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 |
| Alias | Bayesian censored regression, Bayesian Type I Tobit, Bayesian truncated regression, Tobit with priors | Bayesian MLR, Bayesian linear regression, Bayesian multivariate regression, conjugate normal-inverse-gamma regression |
| Närliggande≠ | 5 | 6 |
| Sammanfattning≠ | The Bayesian Tobit model extends Tobin's censored regression framework by replacing maximum-likelihood point estimates with a full posterior distribution over regression coefficients and error variance. By embedding Gibbs sampling with data augmentation, it produces credible intervals, handles small censored samples gracefully, and naturally incorporates prior knowledge about effect sizes. | 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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